Answer to Question #295390 in Statistics and Probability for Adam

Question

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a​ girl, but assume that the method has no​ effect, so the probability of a girl is 0.5. Assume that the groups consist of 17 couples.

Answer 1

Question is incomplete. Assume it as follows:

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a​ girl, but assume that the method has no​ effect, so the probability of a girl is 0.5. Assume that the groups consist of 17 couples. Find the mean for the numbers of girls in groups of 17 births.

Solution:

The mean value of numbers of girls in groups of 43 births is obtained below:

From the given information, the probability that a girl is 50 \% and the groups consists of 43 number of couples.

That is, n=17 and p=0.50

The probability mass function of X is,

 $P(X=x)=\left(\begin{array}{c}17 \\ x\end{array}\right)(0.50)^{x}(1-0.50)^{17-x}$

The required mean is,

$\begin{aligned} E(X) &=n p \\ &=17 \times 0.50 \\ &=8.5 \end{aligned}$