Suppose that a family has 5 children.​ Also, suppose that the probabil

klytamnestra9a

klytamnestra9a

Answered question

2021-11-15

Suppose that a family has 5 children.​ Also, suppose that the probability of having a boy is 12.
Find the probability that the family has at least 4 boys.
The probability that the family has at least 4 boys is?

Answer & Explanation

Roger Noah

Roger Noah

Beginner2021-11-16Added 17 answers

Step 1
The binomial probability distribution is,
P(X=x)=(nx)(p)x(1p)nx
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
Let x be the number of boys in the family which follows binomial distribution with sample size 5 and probability of success 0.5 (=12).
Step 2
The probability that the family has at least 4 boys is,
P(X4)=P(X=4)+P(X=5)
=(54)(0.5)4(10.5)54+(55)(0.5)5(10.5)55
=(5×0.55)+(1×0.55)
=0.15625+0.03125
=0.1875
Thus, the probability that the family has at least 4 boys is 0.1875.

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