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Project: Irving Parada - Laboratorio de Aplicaciones I 22-P/LdeA 22-P

Path: Laboratorio de Aplicaciones I 22-P/Práctica 3: Embarazos no deseados / Embarazos no deseados.ipynb

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Kernel: SageMath 9.1

Practica 3: Embarazos no deseados

For most women, including women who want to have children, contraception is not an option; it is a basic health care necessity.
Louise Slaughter.

La siguiente tabla condensa la eficacia de distintos métodos anticonceptivos de acuerdo con la CDC

Anticonceptivo	$e$	Anticonceptivo	$e$
Implantes	99.9	Diafragma	88
DIU	99.2	Condón Masculino	82
Histeroscopía	99.5	Condón Femenino	79
Vasectomía	99.8	Coito interrumpido	78
Inyectable	94	Esponja	77
Píldoras	91	Calendario	76
Parche	91	Espermicida	72

En general podemos asumir que, para cada pareja existe una constante $f$ , que es llamada fecundabilidad por los demógrafos, que es la probabilidad de que haya un embarazo en un mes para esa pareja. El valor exacto de $f$ depende de muchos factores: la edad, las condiciones biológicas de la pareja, la frecuencia con la que tienen relaciones sexuales, etcétera. Pero en general el valor de $f$ está entre 0.1 y 0.3. Elabora una función llamada embarazo que reciba $f$ y regrese 1 si al final del mes hay un embarazo y 0 en caso contrario. Para hacer esto debes de comparar $f$ con un número aleatorio, que puedes obtener con la función random( ). Si el numero aleatorio es menor que f, entonces hay un embarazo.

In [3]:

def embarazo(f):
    x=random()
    if (x<=f):
        return 1
    else:
        return 0

In [4]:

embarazo(0.5)

1

Ahora elabora una función meses que reciba $f$ y calcule el número de meses que va a tardar la pareja en que haya concepción.

In [5]:

def meses(f):
    mes=0
    while(embarazo(f)==0):
        mes=mes+1
    return mes

Para $f=0.2$ simula 10001 veces este experimento y calcula la media, la mediana y la moda.

In [6]:

L=[meses(0.2) for i in srange(10000)]
print(L)

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3, 1, 5, 11, 1, 2, 7, 0, 1, 0, 4, 0, 7, 0, 8, 1, 4, 2, 8, 1, 1, 3, 6, 1, 3, 33, 1, 0, 0, 2, 2, 8, 1, 5, 3, 3, 2, 2, 0, 1, 5, 1, 2, 8, 0, 7, 3, 4, 8, 5, 2, 2, 2, 0, 7, 4, 3, 15, 1, 9, 12, 2, 0, 0, 11, 2, 4, 2, 3, 0, 3, 1, 2, 0, 11, 0, 2, 1, 3, 0, 5, 1, 12, 5, 2, 3, 3, 2, 5, 2, 15, 4, 3, 2, 5, 0, 11, 0, 0, 3, 1, 1, 5, 13, 4, 0, 5, 2, 5, 1, 4, 0, 7, 7, 1, 2, 4, 0, 0, 1, 0, 17, 1, 0, 8, 5, 7, 1, 1, 0, 0, 1, 6, 0, 1, 0, 4, 2, 1, 2, 7, 1, 1, 3, 2, 1, 0, 0, 4, 0, 0, 5, 0, 0, 2, 0, 1, 7, 2, 0, 5, 4, 1, 2, 11, 8, 3, 0, 9, 2, 4, 1, 1, 2, 2, 6, 2, 23, 2, 7, 24, 5, 4, 1, 18, 7, 2, 3, 3, 1, 3, 8, 6, 3, 9, 9, 1, 1, 2, 11, 8, 3, 3, 5, 5, 3, 2, 0, 1, 10, 1, 0, 6, 7, 0, 1, 4, 2, 0, 0, 3, 0, 0, 8, 3, 1, 15, 0, 7, 9, 0, 0, 6, 4, 3, 3, 3, 13, 1, 3, 3, 4, 0, 0, 8, 1, 1, 18, 4, 6, 1, 10, 10, 6, 4, 0, 5, 14, 11, 0, 5, 2, 11, 1, 0, 4, 0, 9, 9, 1, 2, 1, 1, 1, 4, 5, 6, 3, 6, 2, 4, 0, 0, 19, 4, 0, 15, 0, 5, 1, 1, 0, 3, 0, 3, 18, 12, 2, 2, 0, 9, 3, 13, 3, 1, 1, 3, 7, 4, 4, 2, 5, 2, 12, 0, 10, 5, 7, 0, 5, 3, 1, 6, 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0, 2, 1, 0, 0, 6, 1, 2, 11, 10, 9]

¿Que interpretación le puedes dar a la media, la mediana y la moda?

In [7]:

print("media:",mean(L))
print("mediana:",median(L))
print("moda:", mode(L))

media: 7971/2000
mediana: 3
moda: [0]

Grafica para los valores de los puntos de la forma $(f,\bar{x}_f)$ para $f=0.10, 0.11, 0.12, 0.13 ... , 0.29, 0.30$ . Donde $x_f$ es la media de 10001 simulaciones para cierta $f$ ¿Qué forma tiene la función?

In [8]:

def media(f):
    L=[meses(f)for i in srange(10000)]
    return mean(L)
puntos=[[f, media(f)] for f in srange (.10,.31,.01)]
line(puntos)

Calcula, mediante una simulación de 10001 casos, cual es la probabilidad de que en menos de un año una pareja tenga un embarazo para una cierta $f=.2$

In [9]:

L=[meses(.2) for i in srange(10001)]
cont=0
for x in L:
    if x<=11:
        cont=cont+1
print(N(cont/10001))

0.932506749325067

Desde un enfoque matemático, los anticonceptivos refinan el concepto de fecundabilidad. Dado que la fecundabilidad $f$ es la probabilidad de concebir en un cierto mes, un anticonceptivo nulifica una cierta fracción $e$ de la fecundabilidad natural. La fracción restante $p$ sería la fecundabilidad real, con anticonceptivos, del mes asumiendo que la pareja usa el mismo método anticonceptivo durante todo el mes. En este sentido tendríamos que $p=f - ef$ Donde $e$ es la eficacia del anticonceptivo

In [10]:

def condonchui(f):
    P=0.2- f*(0.2)
    return P

In [11]:

condonchui(.82)

0.0360000000000000

Considerando como método anticonceptivo el condon masculino, y $f=0.2$ simula 10001 veces el experimento y encuentra la media, mediana y moda de los experimentos.

In [12]:

L=[meses(condonchui(0.86)) for i in srange(10001)]
print(L)

[51, 5, 22, 20, 26, 18, 126, 20, 119, 56, 8, 32, 20, 3, 10, 7, 2, 19, 9, 6, 13, 9, 3, 56, 6, 48, 19, 171, 49, 12, 2, 80, 1, 43, 11, 26, 8, 28, 2, 21, 1, 5, 18, 19, 29, 53, 1, 129, 1, 5, 4, 7, 31, 47, 34, 2, 16, 10, 18, 7, 1, 20, 33, 198, 8, 13, 27, 251, 69, 23, 36, 35, 3, 39, 13, 29, 34, 11, 50, 4, 55, 61, 12, 23, 13, 38, 19, 18, 15, 21, 71, 3, 1, 7, 60, 37, 18, 22, 53, 1, 36, 209, 33, 19, 229, 3, 9, 28, 14, 2, 42, 22, 42, 75, 25, 0, 51, 19, 21, 2, 9, 29, 28, 11, 0, 22, 13, 57, 24, 21, 28, 11, 26, 11, 9, 10, 11, 70, 42, 6, 74, 28, 8, 12, 25, 73, 8, 58, 10, 134, 28, 47, 59, 37, 9, 17, 41, 31, 35, 26, 49, 86, 37, 36, 2, 11, 27, 22, 39, 9, 34, 50, 7, 16, 8, 38, 70, 9, 12, 102, 18, 15, 4, 5, 79, 84, 37, 54, 31, 18, 13, 42, 43, 111, 16, 5, 66, 102, 7, 18, 156, 48, 26, 108, 11, 10, 31, 27, 12, 8, 70, 92, 94, 24, 29, 65, 12, 32, 31, 9, 11, 93, 24, 10, 6, 7, 0, 6, 83, 44, 22, 12, 3, 10, 3, 40, 14, 66, 5, 19, 1, 39, 10, 14, 30, 92, 24, 15, 100, 15, 0, 1, 19, 26, 107, 0, 34, 29, 70, 97, 58, 13, 29, 24, 6, 22, 111, 10, 177, 4, 9, 21, 9, 13, 3, 5, 133, 45, 4, 15, 4, 32, 48, 12, 60, 6, 133, 18, 6, 4, 13, 12, 1, 18, 19, 14, 17, 206, 11, 66, 33, 2, 5, 56, 40, 12, 25, 62, 4, 5, 4, 20, 5, 0, 34, 17, 15, 1, 8, 5, 107, 6, 81, 18, 8, 26, 21, 1, 16, 111, 3, 14, 20, 37, 23, 8, 4, 5, 78, 14, 48, 80, 55, 5, 0, 67, 16, 2, 3, 0, 20, 58, 53, 1, 103, 22, 37, 42, 47, 27, 56, 2, 6, 97, 34, 32, 18, 42, 19, 21, 96, 70, 51, 39, 7, 95, 165, 23, 2, 70, 36, 41, 62, 3, 12, 4, 57, 19, 14, 147, 76, 30, 4, 8, 19, 54, 87, 7, 0, 29, 18, 5, 38, 8, 4, 15, 27, 12, 37, 59, 134, 4, 74, 8, 80, 41, 7, 12, 17, 20, 2, 25, 102, 6, 34, 55, 18, 6, 71, 31, 36, 59, 48, 71, 22, 16, 75, 22, 22, 21, 57, 49, 19, 20, 17, 31, 26, 3, 20, 2, 13, 62, 52, 110, 54, 55, 134, 28, 79, 19, 24, 8, 8, 47, 70, 9, 50, 17, 3, 22, 29, 3, 24, 1, 23, 12, 13, 6, 26, 101, 55, 24, 62, 31, 98, 152, 18, 39, 40, 25, 11, 69, 88, 76, 41, 3, 5, 18, 33, 44, 29, 5, 8, 60, 6, 5, 63, 20, 33, 8, 54, 97, 19, 36, 20, 55, 31, 3, 9, 26, 54, 15, 38, 22, 39, 28, 37, 25, 14, 40, 16, 8, 5, 60, 1, 11, 93, 4, 157, 66, 7, 21, 25, 13, 4, 10, 33, 34, 7, 38, 3, 12, 57, 36, 14, 25, 190, 81, 3, 1, 2, 38, 3, 50, 8, 25, 9, 3, 22, 45, 64, 19, 34, 16, 81, 3, 0, 6, 34, 0, 53, 47, 43, 41, 1, 26, 40, 125, 14, 43, 65, 4, 31, 10, 195, 76, 26, 1, 2, 44, 13, 59, 31, 28, 44, 78, 78, 92, 48, 9, 29, 1, 28, 19, 39, 29, 45, 7, 1, 70, 1, 17, 44, 14, 72, 44, 3, 24, 51, 97, 2, 8, 13, 9, 78, 25, 107, 14, 67, 36, 14, 11, 16, 9, 38, 0, 67, 1, 16, 0, 17, 81, 10, 66, 3, 38, 25, 6, 24, 54, 94, 69, 5, 8, 6, 19, 11, 61, 32, 21, 35, 57, 27, 12, 45, 8, 74, 8, 14, 2, 111, 15, 35, 20, 23, 11, 16, 0, 51, 33, 11, 11, 63, 3, 18, 16, 75, 16, 3, 68, 247, 4, 9, 20, 12, 52, 1, 30, 19, 21, 92, 26, 79, 54, 9, 35, 11, 51, 50, 36, 24, 6, 37, 24, 28, 9, 25, 21, 46, 102, 3, 36, 5, 1, 3, 32, 53, 30, 5, 28, 64, 99, 28, 52, 27, 73, 90, 17, 33, 4, 10, 63, 76, 5, 5, 16, 21, 47, 57, 67, 77, 17, 12, 37, 14, 64, 8, 51, 30, 4, 9, 7, 113, 20, 76, 10, 43, 0, 51, 48, 10, 6, 16, 99, 22, 9, 112, 44, 64, 28, 23, 33, 45, 61, 5, 122, 53, 15, 58, 233, 183, 114, 12, 55, 32, 9, 10, 0, 46, 97, 42, 49, 11, 46, 4, 22, 5, 0, 8, 15, 4, 24, 15, 44, 78, 26, 21, 115, 12, 23, 6, 49, 75, 26, 70, 2, 81, 34, 63, 16, 0, 30, 9, 92, 113, 32, 123, 52, 93, 53, 27, 42, 26, 16, 35, 145, 1, 5, 44, 42, 17, 6, 32, 27, 26, 53, 1, 19, 33, 27, 7, 24, 26, 29, 5, 215, 27, 23, 4, 0, 37, 13, 9, 22, 19, 6, 6, 59, 14, 43, 15, 51, 5, 20, 120, 24, 78, 19, 16, 11, 11, 12, 61, 10, 18, 47, 76, 0, 14, 36, 82, 3, 54, 73, 5, 23, 16, 29, 11, 17, 16, 26, 135, 11, 2, 21, 9, 27, 131, 25, 5, 26, 52, 40, 7, 59, 5, 1, 12, 26, 14, 0, 12, 91, 6, 7, 1, 15, 13, 57, 2, 8, 24, 1, 15, 37, 106, 21, 43, 9, 27, 14, 48, 57, 49, 25, 25, 70, 30, 20, 7, 6, 0, 5, 14, 8, 23, 57, 49, 17, 29, 16, 16, 15, 27, 24, 1, 117, 22, 79, 4, 19, 35, 43, 43, 23, 0, 43, 73, 0, 23, 25, 2, 3, 12, 33, 24, 4, 119, 2, 16, 8, 42, 35, 14, 38, 13, 9, 19, 3, 19, 6, 0, 6, 21, 18, 48, 9, 12, 19, 10, 62, 1, 17, 25, 154, 0, 3, 23, 10, 4, 25, 12, 87, 18, 35, 45, 1, 27, 1, 22, 51, 67, 8, 7, 99, 1, 3, 10, 8, 74, 28, 11, 29, 29, 3, 66, 44, 11, 38, 91, 4, 28, 25, 0, 11, 8, 11, 70, 20, 74, 69, 19, 48, 0, 6, 1, 10, 12, 129, 12, 0, 40, 47, 84, 9, 3, 63, 0, 94, 94, 11, 17, 8, 2, 22, 46, 22, 71, 61, 41, 30, 7, 46, 3, 214, 105, 39, 8, 71, 30, 20, 27, 11, 35, 2, 73, 42, 38, 25, 68, 130, 15, 6, 78, 32, 50, 6, 20, 1, 9, 11, 6, 0, 38, 72, 7, 86, 44, 54, 53, 80, 8, 0, 68, 23, 18, 146, 3, 22, 1, 29, 105, 44, 19, 36, 25, 1, 7, 5, 10, 15, 10, 2, 58, 37, 15, 6, 25, 13, 30, 24, 19, 13, 86, 98, 4, 50, 3, 145, 59, 11, 19, 28, 15, 38, 2, 9, 115, 24, 8, 25, 68, 0, 24, 21, 9, 1, 51, 1, 28, 25, 38, 0, 24, 26, 119, 4, 69, 8, 38, 27, 15, 25, 197, 36, 9, 144, 39, 10, 52, 25, 53, 17, 28, 8, 7, 32, 16, 43, 10, 2, 42, 8, 46, 53, 30, 55, 10, 13, 11, 47, 65, 35, 5, 11, 113, 43, 29, 73, 40, 156, 17, 16, 14, 8, 10, 12, 69, 45, 23, 3, 121, 32, 16, 69, 24, 32, 26, 13, 0, 23, 52, 2, 3, 34, 18, 17, 64, 157, 0, 33, 35, 97, 33, 2, 35, 62, 19, 56, 30, 55, 37, 7, 36, 20, 70, 12, 55, 120, 11, 22, 49, 44, 19, 23, 1, 39, 4, 98, 14, 13, 15, 96, 34, 72, 6, 0, 43, 66, 40, 56, 3, 46, 71, 25, 50, 11, 29, 104, 24, 42, 45, 72, 62, 59, 27, 35, 18, 104, 0, 16, 136, 37, 22, 26, 5, 44, 15, 51, 2, 25, 34, 52, 25, 3, 36, 10, 63, 82, 71, 25, 48, 24, 17, 22, 4, 28, 5, 29, 117, 84, 87, 141, 7, 71, 3, 51, 35, 16, 7, 29, 10, 64, 38, 11, 41, 1, 99, 40, 23, 33, 14, 83, 4, 17, 35, 17, 12, 97, 7, 12, 108, 73, 119, 46, 27, 41, 9, 12, 55, 23, 39, 10, 30, 26, 36, 9, 16, 77, 89, 3, 52, 56, 21, 2, 118, 92, 16, 5, 101, 62, 115, 25, 18, 33, 6, 6, 2, 3, 32, 72, 19, 54, 37, 26, 44, 12, 9, 18, 26, 4, 2, 16, 0, 130, 2, 7, 16, 6, 39, 21, 73, 9, 58, 71, 24, 74, 98, 19, 12, 100, 36, 23, 23, 1, 18, 17, 67, 7, 20, 2, 0, 9, 25, 50, 50, 45, 132, 8, 42, 15, 10, 84, 37, 55, 62, 17, 2, 40, 3, 66, 30, 62, 4, 81, 12, 98, 61, 81, 54, 15, 3, 17, 54, 22, 111, 31, 7, 4, 8, 1, 12, 25, 96, 23, 125, 21, 83, 65, 9, 57, 6, 75, 124, 80, 50, 87, 28, 5, 194, 7, 25, 20, 4, 0, 60, 4, 115, 135, 31, 79, 171, 25, 155, 53, 29, 6, 15, 7, 117, 103, 21, 25, 87, 14, 9, 10, 161, 70, 15, 36, 56, 36, 81, 11, 0, 3, 53, 16, 31, 49, 27, 0, 8, 68, 25, 33, 20, 120, 44, 10, 68, 48, 9, 7, 54, 10, 41, 24, 17, 11, 15, 58, 4, 20, 39, 5, 50, 16, 35, 10, 25, 30, 51, 34, 171, 18, 157, 6, 123, 9, 75, 18, 10, 6, 54, 153, 9, 60, 0, 20, 26, 39, 22, 61, 45, 9, 11, 24, 33, 0, 36, 17, 32, 7, 69, 234, 15, 2, 34, 59, 1, 3, 39, 21, 65, 32, 38, 8, 1, 37, 44, 13, 62, 47, 1, 53, 24, 67, 58, 26, 1, 18, 17, 54, 8, 3, 10, 31, 51, 58, 49, 92, 81, 109, 10, 16, 55, 43, 0, 31, 42, 8, 33, 28, 0, 74, 19, 98, 10, 67, 83, 17, 53, 44, 5, 22, 31, 21, 47, 38, 27, 47, 14, 10, 84, 9, 0, 1, 13, 11, 17, 26, 75, 8, 5, 73, 0, 11, 109, 61, 90, 10, 62, 1, 55, 37, 85, 8, 0, 8, 32, 20, 21, 157, 54, 8, 86, 10, 5, 26, 31, 90, 26, 17, 19, 15, 35, 23, 19, 25, 0, 17, 37, 33, 5, 149, 221, 54, 71, 14, 63, 29, 12, 3, 52, 25, 14, 0, 87, 11, 32, 73, 2, 2, 48, 66, 16, 16, 13, 97, 47, 0, 4, 114, 10, 27, 15, 11, 34, 38, 0, 51, 78, 19, 11, 103, 6, 20, 8, 143, 19, 52, 31, 15, 31, 9, 7, 1, 15, 4, 1, 8, 48, 14, 6, 8, 92, 47, 36, 28, 14, 155, 77, 2, 96, 65, 36, 6, 6, 66, 34, 26, 50, 62, 47, 7, 47, 24, 111, 31, 92, 40, 17, 8, 4, 10, 28, 23, 28, 118, 13, 14, 6, 26, 22, 8, 29, 83, 9, 24, 0, 95, 31, 145, 30, 42, 79, 6, 3, 0, 56, 2, 8, 2, 23, 2, 4, 15, 27, 41, 94, 49, 15, 8, 34, 43, 7, 0, 22, 19, 11, 25, 21, 41, 25, 4, 57, 100, 0, 8, 24, 56, 5, 1, 3, 67, 14, 2, 12, 4, 33, 3, 18, 5, 37, 8, 21, 0, 15, 14, 17, 15, 1, 22, 1, 15, 44, 33, 19, 52, 1, 5, 0, 66, 5, 110, 22, 51, 51, 37, 137, 80, 93, 1, 2, 53, 4, 54, 6, 9, 4, 83, 42, 76, 21, 20, 21, 85, 2, 32, 93, 14, 2, 8, 1, 69, 3, 18, 49, 13, 47, 20, 78, 18, 47, 0, 36, 25, 53, 13, 23, 28, 42, 69, 54, 10, 8, 67, 84, 10, 32, 30, 35, 30, 39, 28, 39, 219, 22, 74, 12, 22, 27, 39, 11, 18, 2, 39, 1, 5, 1, 6, 13, 133, 16, 76, 12, 1, 99, 97, 24, 41, 73, 4, 98, 18, 11, 4, 51, 122, 12, 4, 86, 127, 31, 61, 18, 0, 14, 20, 12, 38, 119, 58, 27, 49, 66, 92, 49, 18, 72, 36, 1, 31, 7, 27, 26, 19, 2, 31, 48, 13, 57, 76, 5, 5, 137, 44, 13, 64, 58, 22, 53, 15, 39, 22, 7, 85, 34, 117, 22, 5, 32, 26, 13, 138, 26, 109, 36, 58, 98, 40, 1, 12, 19, 53, 46, 34, 12, 47, 82, 19, 57, 4, 39, 12, 16, 19, 54, 0, 51, 36, 52, 37, 7, 6, 23, 79, 20, 30, 33, 85, 75, 50, 37, 123, 2, 30, 17, 17, 72, 31, 20, 38, 51, 43, 17, 16, 131, 35, 55, 34, 180, 71, 6, 89, 81, 0, 74, 15, 3, 7, 28, 3, 5, 11, 2, 102, 8, 11, 47, 31, 9, 41, 9, 42, 18, 31, 28, 22, 0, 37, 29, 98, 11, 38, 80, 19, 59, 11, 120, 5, 124, 41, 3, 27, 10, 11, 39, 18, 33, 72, 24, 3, 48, 65, 4, 8, 96, 1, 10, 38, 49, 191, 14, 8, 90, 79, 9, 3, 15, 8, 161, 44, 3, 22, 62, 2, 70, 158, 59, 54, 29, 5, 12, 51, 8, 28, 0, 37, 41, 12, 43, 19, 0, 4, 43, 62, 20, 36, 109, 4, 5, 10, 51, 8, 47, 0, 23, 77, 17, 74, 41, 9, 2, 10, 2, 91, 13, 32, 17, 21, 57, 33, 88, 24, 35, 26, 172, 2, 8, 64, 25, 24, 94, 95, 15, 64, 44, 1, 21, 51, 0, 10, 38, 103, 32, 33, 30, 60, 10, 10, 54, 38, 11, 21, 31, 17, 25, 27, 29, 20, 7, 189, 0, 20, 27, 6, 23, 6, 87, 26, 3, 46, 12, 18, 10, 14, 18, 5, 3, 11, 71, 30, 29, 86, 16, 16, 10, 35, 41, 39, 8, 46, 48, 33, 21, 71, 3, 80, 27, 62, 45, 34, 44, 5, 14, 17, 52, 14, 13, 80, 3, 38, 1, 16, 9, 22, 19, 73, 39, 21, 36, 101, 70, 17, 15, 40, 62, 56, 47, 72, 31, 38, 20, 25, 6, 9, 0, 23, 5, 11, 7, 0, 18, 13, 53, 17, 65, 1, 38, 17, 20, 9, 45, 111, 145, 89, 0, 12, 35, 32, 63, 75, 37, 7, 38, 124, 60, 13, 32, 0, 8, 27, 35, 17, 10, 18, 16, 39, 20, 37, 178, 6, 12, 4, 3, 16, 7, 22, 12, 3, 111, 16, 141, 63, 8, 15, 57, 23, 21, 50, 1, 107, 0, 10, 7, 37, 37, 17, 22, 21, 113, 70, 19, 8, 41, 44, 31, 12, 17, 47, 6, 52, 68, 56, 199, 7, 13, 51, 0, 42, 32, 27, 61, 2, 12, 13, 11, 52, 11, 22, 11, 76, 30, 131, 17, 48, 31, 87, 9, 32, 23, 79, 13, 17, 10, 27, 94, 22, 91, 23, 10, 16, 10, 5, 25, 6, 96, 38, 7, 153, 71, 15, 8, 123, 68, 47, 68, 8, 0, 30, 5, 20, 15, 22, 0, 60, 31, 21, 54, 20, 11, 41, 29, 17, 9, 12, 17, 14, 9, 10, 1, 0, 26, 4, 27, 14, 7, 54, 75, 5, 34, 17, 13, 94, 24, 6, 8, 21, 7, 59, 59, 5, 1, 19, 20, 45, 18, 44, 59, 66, 53, 28, 12, 1, 14, 41, 32, 39, 6, 60, 11, 0, 4, 69, 157, 8, 81, 53, 25, 11, 1, 87, 5, 62, 16, 25, 47, 28, 66, 18, 2, 8, 15, 10, 31, 41, 67, 65, 5, 30, 18, 8, 40, 60, 28, 15, 50, 3, 32, 4, 50, 47, 34, 15, 15, 12, 87, 26, 11, 20, 4, 9, 34, 56, 42, 19, 2, 25, 72, 66, 18, 20, 13, 31, 0, 3, 12, 51, 11, 81, 28, 33, 53, 26, 9, 27, 77, 11, 5, 131, 8, 7, 36, 15, 28, 30, 31, 30, 39, 104, 71, 3, 27, 16, 2, 47, 18, 22, 20, 6, 3, 39, 59, 25, 14, 12, 0, 4, 10, 2, 14, 40, 124, 40, 48, 11, 39, 25, 4, 120, 61, 44, 92, 7, 80, 3, 12, 4, 11, 75, 3, 24, 6, 33, 27, 2, 5, 46, 105, 10, 127, 6, 21, 13, 8, 21, 27, 11, 62, 114, 13, 4, 53, 21, 16, 15, 16, 5, 10, 39, 46, 0, 9, 8, 8, 63, 6, 20, 7, 93, 46, 74, 2, 23, 36, 3, 66, 42, 58, 8, 40, 28, 6, 10, 127, 2, 15, 29, 18, 87, 8, 36, 16, 69, 12, 61, 54, 65, 3, 2, 22, 75, 11, 32, 33, 114, 9, 81, 11, 18, 94, 21, 23, 25, 27, 39, 11, 4, 79, 30, 92, 1, 0, 12, 5, 13, 4, 9, 68, 15, 19, 5, 31, 7, 7, 7, 85, 6, 7, 179, 13, 4, 8, 27, 14, 120, 4, 5, 18, 5, 51, 9, 19, 1, 11, 2, 6, 13, 4, 17, 13, 95, 32, 48, 0, 10, 5, 33, 52, 31, 25, 162, 77, 63, 6, 16, 28, 9, 54, 39, 7, 26, 22, 48, 3, 6, 16, 9, 19, 8, 59, 83, 6, 50, 7, 72, 23, 1, 23, 71, 102, 23, 8, 2, 25, 164, 43, 28, 6, 32, 77, 17, 27, 18, 10, 35, 74, 5, 11, 24, 0, 27, 3, 76, 38, 20, 28, 78, 14, 119, 51, 52, 8, 15, 73, 105, 24, 107, 0, 27, 5, 4, 96, 40, 12, 50, 0, 15, 19, 35, 14, 6, 52, 4, 18, 31, 37, 2, 81, 3, 18, 18, 0, 25, 5, 16, 118, 13, 10, 37, 64, 18, 4, 46, 43, 83, 31, 16, 107, 10, 5, 52, 211, 57, 32, 48, 0, 7, 29, 2, 7, 19, 9, 17, 3, 65, 269, 11, 45, 14, 2, 33, 8, 8, 29, 44, 22, 1, 17, 21, 6, 0, 97, 11, 1, 27, 10, 14, 53, 90, 15, 150, 10, 115, 19, 97, 21, 66, 12, 158, 30, 19, 129, 23, 36, 26, 4, 1, 2, 83, 42, 23, 63, 3, 17, 38, 0, 69, 165, 10, 4, 38, 20, 8, 68, 42, 125, 13, 23, 19, 5, 22, 22, 9, 59, 129, 22, 13, 34, 51, 15, 22, 6, 59, 28, 1, 51, 8, 44, 10, 4, 71, 55, 6, 58, 95, 45, 88, 60, 17, 17, 3, 36, 37, 12, 1, 51, 3, 38, 37, 95, 26, 22, 15, 24, 13, 32, 40, 80, 2, 36, 20, 118, 26, 76, 66, 25, 41, 6, 12, 47, 68, 63, 56, 0, 25, 61, 8, 55, 19, 10, 8, 98, 57, 50, 2, 95, 63, 20, 5, 26, 0, 27, 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4, 5, 2, 18, 42, 8, 13, 2, 31, 11, 26, 1, 0, 5, 25, 40, 8, 54, 9, 45, 21, 0, 44, 79, 6, 61, 97, 94, 19, 37, 8, 54, 17, 3, 10, 26, 46, 20, 44, 7, 112, 3, 32, 64, 134, 10, 3, 38, 12, 33, 12, 32, 145, 15, 99, 85, 10, 43, 59, 2, 18, 104, 7, 10, 6, 49, 2, 7, 79, 16, 3, 10, 94, 8, 38, 84, 35, 1, 3, 3, 47, 5, 22, 38, 64, 15, 33, 4, 76, 46, 35, 92, 5, 18, 11, 42, 46, 58, 5, 113, 9, 11, 10, 14, 74, 17, 0, 27, 6, 61, 137, 15, 35, 11, 72, 45, 0, 5, 80, 2, 1, 54, 35, 8, 4, 51, 23, 8, 25, 2, 9, 93, 122, 56, 35, 7, 18, 8, 16, 42, 3, 18, 5, 53, 123, 78, 115, 28, 1, 53, 8, 21, 25, 73, 2, 22, 40, 13, 15, 56, 19, 4, 4, 91, 164, 55, 17, 31, 30, 2, 7, 38, 49, 40, 74, 13, 44, 35, 71, 11, 52, 35, 61, 2, 39, 57, 61, 51, 12, 35, 131, 8, 54, 5, 23, 11, 46, 13, 56, 36, 28, 22, 13, 25, 51, 21, 201, 38, 0, 55, 7, 46, 43, 16, 31, 17, 20, 25, 44, 15, 56, 38, 3, 23, 25, 12, 122, 11, 20, 9, 15, 8, 10, 53, 4, 61, 16, 5, 40, 38, 35, 67, 15, 50, 0, 15, 31, 78, 28, 24, 21, 13, 10, 13, 17, 1, 23, 40, 90, 96, 41, 10, 10, 104, 4, 8, 7, 39, 7, 8, 18, 20, 25, 46, 8, 20, 26, 45, 13, 143, 11, 19, 124, 25, 27, 32, 62, 61, 27, 29, 37, 115, 116, 0, 0, 32, 7, 53, 2, 43, 8, 66, 15, 4, 88, 21, 2, 29, 53, 85, 66, 70, 60, 11, 2, 3, 61, 10, 1, 63, 11, 10, 78, 93, 72, 22, 2, 92, 9, 21, 35, 59, 10, 25, 111, 84, 91, 143, 37, 22, 35, 43, 31, 103, 57, 4, 54, 57, 42, 43, 6, 48, 1, 38, 14, 14, 16, 124, 7, 12, 1, 1, 29, 57, 6, 73, 20, 8, 92, 55, 59, 22, 33, 18, 5, 11, 0, 76, 4, 89, 18, 14, 33, 62, 5, 20, 47, 11, 59, 26, 52, 55, 30, 10, 15, 2, 43, 45, 26, 95, 14, 54, 10, 88, 48, 4, 66, 4, 48, 2, 93, 67, 0, 55, 36, 7, 20, 36, 16, 52, 1, 78, 5, 31, 14, 7, 0, 31, 3, 0, 3, 19, 51, 14, 4, 43, 63, 27, 73, 1, 119, 0, 1, 42, 62, 23, 5, 71, 27, 22, 23, 32, 9, 22, 39, 58, 4, 6, 17, 8, 5, 21, 100, 86, 13, 58, 6, 2, 21, 135, 87, 27, 15, 23, 9, 3, 76, 49, 59, 13, 0, 39, 29, 7, 7, 69, 25, 95, 95, 35, 50, 50, 76, 36, 27, 67, 44, 31, 5, 50, 43, 82, 207, 77, 40, 111, 50, 21, 51, 86, 16, 6, 0, 37, 41, 52, 20, 135, 17, 54, 3, 0, 7, 34, 93, 145, 62, 50, 82, 19, 9, 1, 86, 34, 47, 4, 82, 40, 57, 28, 8, 122, 58, 118, 11, 30, 55, 2, 4, 55, 106, 52, 25, 96, 10, 13, 2, 20, 9, 41, 3, 27, 85, 67, 40, 12, 53, 30, 2, 123, 20, 66, 95, 3, 16, 19, 0, 6, 47, 45, 44, 18, 4, 2, 95, 9, 2, 2, 13, 31, 42, 35, 29, 49, 7, 9, 5, 16, 50, 14, 31, 36, 69, 52, 37, 6, 40, 7, 43, 51, 20, 21, 49, 0, 55, 11, 14, 57, 5, 90, 2, 5, 17, 6, 6, 31, 72, 21, 3, 26, 17, 0, 51, 7, 64, 17, 5, 8, 5, 110, 40, 51, 48, 73, 31, 43, 5, 27, 39, 27, 6, 7, 17, 33, 104, 45, 68, 39, 15, 90, 26, 7, 1, 33, 25, 3, 56, 70, 20, 1, 30, 21, 43, 10, 27, 9, 80, 30, 4, 6, 70, 48, 11, 7, 14, 8, 2, 1, 4, 31, 15, 22, 94, 98, 18, 18, 50, 16, 18, 17, 42, 24, 1, 5, 58, 51, 149, 0, 66, 7, 21, 30, 8, 103, 11, 0, 27, 134, 21, 53, 106, 13, 12, 9, 1, 56, 9, 30, 32, 6, 2, 27, 169, 12, 12, 95, 27, 22, 154, 68, 44, 61, 23, 58, 25, 10, 76, 3, 20, 56, 4, 25, 71, 198, 39, 95, 11, 8, 57, 9, 114, 104, 26, 3, 24, 3, 117, 5, 12, 14, 36, 12, 22, 69, 142, 135, 64, 131, 45, 0, 40, 17, 39, 15, 56, 28, 1, 39, 12, 17, 38, 6, 58, 27, 0, 33, 35, 89, 20, 81, 11, 1, 4, 18, 104, 40, 8, 55, 5, 152, 1, 3, 56, 15, 22, 9, 26, 30, 8, 49, 0, 6, 89, 6, 9, 21, 4, 6, 25, 19, 1, 8, 2, 75, 18, 35, 141, 33, 16, 2, 5, 40, 47, 1, 150, 27, 79, 0, 22, 10, 31, 61, 30, 54, 63, 12, 22, 24, 30, 101, 69, 2, 79, 45, 28, 4, 1, 65, 7, 36, 10, 34, 76, 11, 20, 8, 4, 31, 19, 57, 18, 1, 4, 36, 10, 19, 39, 46, 41, 10, 25, 6, 14, 19, 1, 17, 23, 12, 26, 66, 21, 45, 3, 20, 19, 4, 5, 29, 84, 12, 50, 4, 52, 0, 3, 136, 23, 8, 11, 104, 20, 8, 15, 20, 55, 10, 2, 31, 18, 34, 21, 22, 88, 23, 0, 8, 1, 11, 1, 84, 55, 1, 49, 25, 10, 0, 10, 42, 15, 0, 32, 63, 15, 91, 28, 22, 20, 19, 85, 74, 0, 25, 25, 11, 24, 24, 34, 30, 35, 21, 9, 68, 35, 51, 144, 2, 0, 16, 40, 30, 55, 66, 100, 76, 77, 17, 86, 54, 25, 12, 113, 11, 80, 13, 6, 25, 5, 25, 12, 5, 52, 32, 23, 21, 24, 23, 4, 21, 20, 41, 32, 1, 31, 110, 0, 49, 49, 63, 60, 31, 140, 0, 10, 39, 3, 41, 58, 129, 16, 54, 72, 0, 10, 8, 6, 58, 89, 100, 25, 12, 21, 13, 23, 7, 47, 21, 40, 32, 12, 17, 28, 25, 3, 45, 31, 105, 18, 3, 28, 8, 16, 26, 1, 16, 21, 6, 81, 0, 61, 16, 54, 3, 50, 171, 34, 71, 27, 54, 7, 25, 4, 79, 29, 27, 33, 4, 2, 39, 5, 20, 30, 10, 26, 19, 34, 8, 16, 78, 56, 22, 7, 66, 91, 117, 5, 4, 108, 10, 50, 264, 12, 7, 1, 12, 90, 23, 50, 106, 38, 45, 30, 8, 35, 68, 84, 70, 8, 2, 45, 45, 14, 54, 10, 2, 49, 9, 3, 215, 19, 42, 19, 6, 9, 20, 48, 9, 28, 2, 23, 0, 21, 53, 43, 46, 0, 0, 5, 10, 22, 55, 6, 20, 56, 43, 21, 37, 42, 103, 24, 31, 16, 33, 6, 22, 22, 1, 26, 13, 10, 55, 54, 43, 38, 4, 0, 95, 60, 122, 11, 26, 125, 8, 5, 6, 11, 39, 3, 40, 5, 21, 29, 43, 4, 97, 54, 57, 9, 121, 6, 56, 142, 15, 32, 13, 20, 122, 22, 49, 10, 17, 0, 13, 5, 17, 53, 74, 122, 14, 13, 17, 13, 1, 67, 26, 114, 4, 15, 60, 18, 66, 36, 57, 119, 69, 89, 47, 20, 79, 34, 3, 65, 8, 6, 35, 45, 33, 37, 16, 27, 9, 9, 4, 3, 102, 11, 17, 2, 70, 19, 34, 26, 28, 42, 33, 108, 13, 9, 19, 38, 3, 9, 162, 26, 4, 11, 5, 23, 18, 5, 44, 18, 11, 5, 96, 2, 5, 104, 26, 10, 30, 90, 33, 10, 7, 31, 102, 46, 12, 13, 45, 11, 33, 23, 16, 9, 21, 43, 5, 98, 5, 37, 4, 45, 58, 5, 31, 25, 53, 45, 27, 15, 15, 1, 1, 81, 157, 44, 10, 9, 8, 171, 5, 41, 42, 38, 19, 29, 97, 31, 4, 13, 80, 12, 43, 58, 24, 65, 25, 57, 24, 38, 34, 81, 39, 6, 54, 7, 29, 13, 59, 1, 18, 73, 47, 15, 20, 44, 40, 0, 6, 24, 86, 14, 29, 53, 55, 5, 28, 58, 15, 13, 95, 90, 2, 46, 53, 33, 10, 30, 16, 12, 12, 10, 19, 8, 35, 11, 0, 76, 0, 102, 29, 145, 73, 28, 61, 1, 27, 89, 8, 74, 15, 55, 156, 16, 112, 64, 8, 5, 21, 38, 7, 10, 27, 28, 14, 22, 38, 67, 21, 27, 60, 20, 32, 29, 48, 32, 51, 26, 26, 31, 17, 0, 25, 23, 14, 42, 27, 14, 92, 0, 20, 59, 2, 16, 12, 73, 9, 154, 39, 23, 22, 4, 0, 108, 2, 7, 105, 19, 61, 0, 23, 11, 15, 16, 55, 12, 191, 11, 28, 0, 107, 2, 77, 7, 7, 66, 37, 0, 0, 0, 19, 71, 49, 48, 10, 6, 16, 23, 41, 4, 52, 16, 102, 14, 36, 40, 2, 29, 9, 7, 13, 26, 156, 1, 14, 60, 71, 60, 16, 48, 45, 59, 4, 10, 37, 4, 68, 7, 104, 0, 7, 17, 26, 34, 3, 6, 26, 118, 31, 9, 86, 130, 5, 24, 21, 46, 8, 11, 27, 22, 61, 7, 19, 61, 60, 2, 18, 31, 95, 47, 93, 37, 66, 2, 13, 44, 17, 10, 127, 34, 107, 0, 11, 52, 7, 18, 70, 67, 70, 16, 4, 22, 17, 23, 5, 7, 12, 122, 38, 2, 11, 26, 30, 0, 14, 1, 36, 2, 35, 26, 64, 17, 6, 13, 64, 91, 10, 5, 96, 21, 6, 54, 183, 16, 161, 73, 34, 5, 111, 6, 34, 0, 63, 21, 50, 29, 56, 96, 7, 58, 27, 87, 10, 7, 22, 60, 66, 26, 17, 35, 27, 0, 10, 18, 3, 115, 9, 36, 15, 29, 12, 40, 19, 10, 5, 23, 66, 23, 21, 111, 32, 10, 67, 3, 97, 3, 19, 73, 24, 116, 6, 11, 39, 67, 65, 29, 69, 13, 1, 5, 75, 12, 74, 1, 54, 4, 9, 18, 51, 25, 31, 52, 79, 32, 36, 44, 3, 50, 250, 6, 80, 8, 0, 93, 6, 17, 44, 31, 80, 2, 73, 27, 9, 7, 49, 0, 33, 27, 20, 15, 11, 5, 89, 5, 7, 6, 2, 69, 31, 32, 4, 6, 62, 7, 1, 61, 136, 2, 20, 39, 1, 47, 5, 19, 53, 113, 114, 57, 11, 100, 31, 31, 11, 38, 43, 82, 28, 15, 24, 118, 13, 7, 16, 121, 16, 21, 40, 39, 15, 23, 67, 13, 38, 146, 32, 9, 34, 3, 35, 2, 0, 66, 2, 6, 13, 15, 104, 4, 8, 0, 35, 63, 127, 0, 50, 11, 16, 53, 7, 34, 34, 7, 32, 34, 37, 1, 1, 30, 76, 17, 43, 43, 28, 19, 20, 53, 7, 22, 54, 33, 34, 0, 17, 4, 57, 3, 21, 60, 8, 11, 4, 23, 0, 11, 12, 34, 19, 6, 43, 24, 58, 68, 17, 4, 49, 22, 5, 16, 2, 36, 49, 127, 8, 8, 43, 29, 31, 4, 60, 14, 46, 5, 78, 63, 8, 33, 34, 40, 49, 2, 104, 97, 5, 92, 11, 63, 1, 0, 9, 17, 48, 12, 3, 59, 29, 58, 33, 4, 5, 63, 13, 29, 31, 105, 13, 13, 11, 23, 4, 54, 8, 8, 14, 24, 2, 0, 5, 13, 39, 9, 2, 51, 4, 63, 47, 8, 13, 54, 31, 27, 9, 15, 62, 19, 0, 34, 12, 28, 36, 11, 12, 79, 87, 14, 37, 10, 86, 0, 20, 23, 25, 48, 31, 17, 21, 12, 71, 24, 17, 19, 36, 20, 41, 16, 76, 10, 18, 86, 27, 1, 18, 52, 9, 4, 5, 25, 17, 41, 26, 14, 123, 51, 34, 76, 43, 100, 1, 192, 17, 9, 16, 22, 40, 21, 47, 18, 18, 49, 1, 79, 22, 2, 2, 42, 24, 14, 44, 43, 1, 2, 30, 85, 3, 5, 47, 16, 26, 17, 67, 13, 80, 22, 18, 23, 17, 15, 65, 12, 58, 4, 15, 52, 20, 51, 23, 15, 23, 3, 78, 5, 34, 45, 20, 57, 145, 37, 3, 18, 6, 40, 0, 5, 0, 53, 12, 31, 178, 48, 25, 1, 49, 19, 7, 32, 1, 38, 17, 27, 6, 22, 4, 26, 60, 10, 53, 23, 17, 9, 30, 28, 42, 9, 6, 92, 37, 115, 92, 27, 21, 5, 104, 2, 22, 92, 12, 6, 27, 6, 5, 65, 5, 32, 33, 17, 21, 69, 29, 40, 8, 18, 3, 10, 29, 20, 80, 51, 10, 8, 53, 7, 3, 0, 36, 43, 9, 45, 110, 16, 4, 3, 2, 15, 45, 17, 11, 20, 84, 2, 80, 68, 59, 36, 1, 65, 3, 52, 112, 14, 61, 2, 61, 66, 13, 52, 20, 7, 18, 40, 64, 15, 113, 81, 3, 11, 62, 1, 280, 46, 27, 53, 0, 20, 6, 121, 17, 11, 4, 11, 42, 104, 12, 53, 63, 0, 254, 12, 0, 14, 79, 21, 16, 101, 12, 2, 9, 71, 27, 17, 73, 22, 2, 8, 10, 23, 4, 34, 19, 18, 16, 0, 4, 81, 17, 50, 8, 6, 13, 25, 34, 0, 128, 6, 4, 81, 5, 2, 46, 124, 25, 10, 41, 44, 80, 1, 86, 61, 23, 133, 36, 16, 12, 33, 45, 13, 188, 5, 29, 193, 2, 2, 1, 50, 15, 14, 32, 1, 170, 24, 90, 10, 65, 11, 0, 80, 39, 19, 15, 72, 10, 42, 18, 96, 53, 12, 8, 19, 3, 0, 81, 18, 13, 29, 9, 27, 57, 23, 0, 118, 30, 66, 144, 2, 7, 6, 42, 53, 25, 25, 128, 60, 32, 22, 7, 34, 3, 0, 5, 31, 53, 22, 61, 4, 5, 25, 36, 95, 71, 83, 6, 40, 48, 1, 42, 3, 72, 50, 10, 4, 4, 35, 40, 30, 7, 16, 43, 8, 1, 21, 36, 43, 85, 5, 158, 14, 32, 90, 29, 41, 22, 3, 49, 4, 60, 45, 24, 0, 11, 100, 91, 7, 2, 9, 11, 102, 75, 18, 11, 166, 22, 38, 5, 22, 56, 0, 3, 22, 40, 4, 7, 5, 7, 49, 13, 52, 62, 30, 10, 24, 10, 10, 6, 82, 2, 35, 10, 16, 29, 18, 57, 65, 44, 30, 0, 38, 9, 25, 27, 136, 19, 70, 24, 69, 37, 62, 24, 32, 59, 2, 10, 50, 79, 13, 33, 8, 22, 65, 6, 14, 116, 68, 88, 29, 12, 72, 6, 58, 44, 14, 2, 5, 78, 35, 68, 61, 7, 18, 9, 17, 93, 12, 9, 25, 20, 79, 29, 17, 12, 42, 70, 16, 0, 7, 53, 14, 6, 30, 0, 4, 7, 40, 31, 26, 37, 0, 1, 9, 4, 60, 39, 58, 11, 16, 95, 12, 71, 7, 178, 37, 88, 32, 36, 77, 42, 18, 40, 29, 15, 35, 12, 6, 3, 6, 33, 10, 28, 31, 17, 13, 55, 86, 2, 63, 72, 14, 67, 16, 4, 0, 16, 27, 13, 26, 23, 43, 31, 2, 33, 7, 43, 28, 28, 31, 9, 6, 73, 69, 16, 17, 25, 20, 31, 39, 7, 8, 12, 209, 52, 9, 7, 5, 2, 7, 1, 1, 26, 51, 31, 25, 34, 15, 37, 39, 47, 5, 5, 11, 72, 126, 13, 15, 23, 85, 22, 4, 33, 14, 13, 15, 17, 46, 44, 10, 99, 11, 0, 65, 44, 5, 16, 56, 20, 4, 43, 13, 67, 12, 16, 40, 47, 13, 21, 9, 16, 21, 119, 91, 0, 2, 27, 5, 70, 63, 30, 48, 76, 1, 4, 60, 35, 60, 18, 66, 29, 91, 15, 8, 13, 36, 21, 4, 10, 74, 56, 53, 13, 54, 29, 90, 65, 0, 2, 50, 72, 18, 29, 18, 126, 31, 10, 17, 5, 31, 15, 136, 4, 17, 30, 0, 5, 44, 67, 29, 25, 28, 53, 68, 54, 12, 26, 35, 4, 31, 9, 34, 13, 5, 6, 23, 68, 32, 6, 36, 36, 13, 12, 12, 34, 8, 102, 50, 12, 28, 13, 19, 224, 34, 46, 10, 5, 2, 30, 10, 7, 42, 14, 70, 6, 0, 33, 34, 27, 44, 33, 53, 27, 17, 26, 91, 15, 24, 85, 11, 4, 1, 21, 9, 14, 90, 23, 69, 12, 19, 27, 35, 36, 28, 42, 86, 6, 27, 11, 8, 23, 31, 62, 50, 22, 21, 27, 51, 13, 0, 6, 34, 2, 47, 31, 137, 3, 2, 10, 24, 29, 9, 21, 81, 7, 28, 1, 3, 13, 7, 110, 64, 55, 5, 65, 19, 11, 0, 19, 84, 1, 55, 3, 38, 15, 39, 10, 103, 22, 31, 76, 18, 82, 28, 26, 0, 66, 35, 77, 14, 34, 34, 47, 71, 105, 21, 85, 22, 67, 0, 37, 0, 1, 37, 119, 3, 100, 101, 5, 31, 42, 25, 2, 37, 125, 25, 73, 91, 67, 8, 30, 46, 6, 12, 69, 14, 124, 17, 13, 35, 98, 31, 5, 14, 54, 30, 9, 36, 16, 99, 4, 58, 63, 38, 58, 9, 60, 32, 13, 7, 25, 91, 4, 29, 10, 21, 13, 64, 82, 16, 9, 59, 17, 91, 8, 25, 72, 20, 26, 20, 21, 72, 34, 49, 13, 33, 41, 36, 34, 47, 52, 100, 125, 10, 9, 19, 1, 19, 23, 118, 35, 5, 4, 58, 54, 10, 3, 11, 20, 15, 21, 29, 6, 0, 8, 38, 4, 5, 68, 75, 1]

¿Como se relaciona la media con la $p$ ? ¿Esto sucederá en todos los casos? Haz una gráfica de la $p$ contra la media $\bar{p}$ para los valores de $f$ entre $0.1$ y $0.3$

In [13]:

puntos=[[p, media(p)] for p in srange(.1,.3,.01)]

In [14]:

line(puntos)

Calcula cual es la probabilidad de que en los proximos 5 años, usando condón masculino como método anticonceptivo y $f=0.2$ , no haya embarazo.

In [15]:

L=[meses((1-.82)*(0.2)) for i in srange(10001)]
cont=0
for x in L:
    if x<=59:
        cont=cont+1
print(N(cont/10001))

0.892110788921108

De hecho podemos probar algo muy interesante. ¿Cuál sería el porcentaje de la población que tendría un embarazo en menos de un sexto de la media? Has varios experimentos para comprobarlo.

In [17]:

#Eficacia de inyectable
e1=0.94
#Eficacia de coito interrumpido
e2=0.78  
#Fecundidalidad - sin protección
f=0.2
#Fecundidalidad real - inyectable y coito interrumpido
p1= (1-e1)*(1-e2)*f
#Fecundalidad real - con inyectable
p2= (1-e1)*f
#Experimentos 
L1=[meses(p1) for i in srange(10001)]
L2=[meses(p2) for i in srange(10001)]

#Calculando probabilidad - inyectable y coito interrumpido
count=0
for x in L1:
    if (x<= 6):
        count +=1
print("Probabilidad de embarazo en 6 meses con inyectable y coito interrumpido:", N(count/10001))

#Calculando Probabilidad - inyectable
count=0
for x in L2:
    if(x<=9):
        count +=1
print("Probabilidad de embarazo en 6 meses con inyectable:", N(count/10001))

Probabilidad de embarazo en 6 meses con inyectable y coito interrumpido: 0.0186981301869813
Probabilidad de embarazo en 6 meses con inyectable: 0.117188281171883

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all in one place. Commercial Alternative to JupyterHub.