Question

Find the probability of a couple having a baby boy when their fifth child is born, given that the first four children were all boys. Assume boys and girls are equally like Is the result the same as the probability of getting all boys among five children? 

The probability is _______ (Type an integer or a simplified fraction.) 

Is this result the same as the probability of getting all boys among five children? 

A. Yes. The events are all independent. 

B. Yes. The final result in each case is the same. 

C. No. The two events are complements. 

D. No. The second event involves more possible outcomes.

Answer 1

The probability of a couple having a baby girl when their fifth child is born, given that the first four children were all girls

$=\frac{\left ( \frac{1}{2} \right )^4*\frac{1}{2}}{\left ( \frac{1}{2} \right )^4}$

$=\frac{1}{2}$

=0.5

The probability of getting all girls all among five children

$=\left ( \frac{1}{2} \right )^5$

$=\frac{1}{32}$