First slide

Theorems of probability

Question

A man has 3 pairs of black socks and 2 pairs of brown socks kept together in a box. If he dressed hurriedly in the dark, the probability that after he has put on a black sock, he will then put on another black sock is

Moderate

A

1/3
B

2/3
C

3/5
D

2/15

Solution

$\begin{array}{l} P (B_{1}) = \frac{^{6} C_{1}}{10 C_{1}} = \frac{6}{10} = \frac{3}{5} \\ P (B_{2} / B_{1}) = \frac{5}{9} (B_{2} = black) \\ ∴ P (B_{1} \cap B_{2}) = P (B_{1}) P (B_{2} / B_{1}) = \frac{3}{5} \times \frac{5}{9} = \frac{1}{3} \end{array}$

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