Question

Assume that a gender selection method was used by a couple trying to conceive a girl. Let x be the number of girls in three births. Assuming that the probability of using this gender selection method is 63% effective in conceiving a girl, list the probability distribution of a couple having three children.

x	P(x)
0
1
2
3

(Please show all work.)

Answer 1

Solution:

n = 3

p = 63% = 0.63

binomial probability distribution

Formula:

P_{(k out of n )}= n!*p^k * q^n-k / k! *(n - k)!

P( x = 0 ) = 3!*0.63⁰ * 0.37^3-0 / 0! *(3 - 0)! = 0.0507

P( x = 1 ) = 3!*0.63¹ * 0.37^3-1 / 1! *(3 - 1)! = 0.2587

P( x = 2 ) = 3!*0.63² * 0.37^3-2 / 2! *(3 - 2)! = 0.4406

P( x = 3 ) = 3!*0.63³ * 0.37^3-3 / 3! *(3 - 3)! = 0.2500'

x	P( x )
0	0.0507
1	0.2587
2	0.4406
3	0.2500