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# Health and Wellness Assume that the gender distribution of

ISBN: 9780073534985 75

## Solution for problem 4DP Chapter 4

Elementary Statistics: A Step By Step Approach | 9th Edition

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Problem 4DP

Health and Wellness Assume that the gender distribution of babies is such that one-half the time females are born and one-half the time males are born. In a family of 3 children, what is the probability that all are girls? In a family of 4? Is it unusual that in a family with 4 children all would be girls? In a family of 5?

Step-by-Step Solution:

Step 1 of 4:

In a family the gender distribution of babies is such that one -half the time females are born and one-half the time males are born.

We have to find the following.

In a family of 3 children, the probability that all are girls.In a family of 4 children, the probability that all are girls.We have to determine whether it is an unusual that in a family with 4 children all would be girls.We have to determine whether it is an unusual that in a family with 5 children all would be girls.

Step 2 of 4 :

It is given that, there is equal probability that females are born and males are born.

P (that females are born) = P (that males are born)

=

Here the birth of each children are independent events.

By the multiplication rule of independent events:

1)

In a family of 3 children, the probability that all are girls.

Required probability =

= (

=

= 0.125

Therefore, the probability that all are girls is 0.125.

Step 3 of 4

Step 4 of 4

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