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 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.
