First slide

Theorems of probability

Question

A young couple has two children. The probability that both children are boys, if it is known that atleast one of the children is a boy is

Easy

A

$\frac{1}{4}$
B

$\frac{1}{3}$
C

$\frac{1}{10}$
D

$\frac{1}{20}$

Solution

$\begin{matrix} n (A) = 2_{C_{1}} + 2_{C_{2}} \to b o t h b o y s \\ ↓ \\ O n l y o n e b o y \end{matrix}$
$n (A \cap B) = 2_{C_{2}}$

$P (B / A) = \frac{n (A \cap B)}{n (A)} = \frac{1}{2 + 1} = \frac{1}{3}$

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