SOLUTION: Suppose that a family has 4 children.​ Also, suppose that the probability of having a girl is one half . Find the probability that the family has the following children. Exactl

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose that a family has 4 children.​ Also, suppose that the probability of having a girl is one half . Find the probability that the family has the following children. Exactl      Log On


   

Question 1153298: Suppose that a family has 4 children.​ Also, suppose that the probability of having a girl is one half
. Find the probability that the family has the following children.
Exactly 3 girls and 1 boy
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let x denote the number of girls in n=4 independent births, where each has a probability p-0.5
we denote this by
X~binomial(n=4,p=0.5)

probability of x number of girls is:

P%28X=x%29=nCx%2Ap%5Ex%2A%281-p%29%5E%28n-x%29where nCx=n%21%2F%28x%21%28n-x%29%21%29
P%28X=x%29=%28n%21%2F%28x%21%28n-x%29%21%29%29%2Ap%5Ex%2A%281-p%29%5E%28n-x%29+
P%28X=3%29, n=4, p=0.5
P%28X=3%29=%284%21%2F%283%21%284-3%29%21%29%29%2A0.5%5E3%2A%281-0.5%29%5E%284-3%29
P%28X=3%29=%284%21%2F%283%21%281%29%29%29%2A0.5%5E3%2A%280.5%29%5E%281%29+
P%28X=3%29=%284%2A3%2A2%2F%283%2A2%29%29%2A0.125%2A0.5
P%28X=3%29=4%2A0.0625
P%28X=3%29=0.25