Question

Assume that the birth of a boy or girl to a couple to be equally likely,mutually exclusive exhaustive and independent of the other children in the family for a couple having $6$ children the probability that their 'three oldest are boy'is

• A. $\frac{20}{64}$
• B. $\frac{1}{64}$
• C. $\frac{2}{64}$
• D. $\frac{8}{64}$

Answer 1

The correct option is C $\frac{2}{64}$

Given that the birth of a boy or girl to a couple to be equally likely,

$\left(1\right)$ mutually exclusive

$\left(2\right)$ exhaustive

$\left(3\right)$ independent

$\Rightarrow$ One event does not affect the other

$P\left(E\right)=P\left(B\right).P\left(B\right).P\left(B\right),P\left(BorG\right).P\left(BorG\right)$

$P\left(B\right)=$ probability of boy is $\frac{1}{2}$

$P\left(G\right)=$ probability of girl is $\frac{1}{2}$

$P\left(E\right)=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times 2$ either boy or girls

$=\frac{2}{64}$