Question

Reddy has two pairs of black shoes and three pairs of brown shoes. He also has three pairs of red socks, four pairs of brown socks and six pairs of black socks. If Reddy chooses a pair of shoes at random and a pair of socks at random, Using Tree Diagram find the probability that he chooses shoes and socks of the same colour?

• A. $\frac{4}{13}$
• B. $\frac{24}{65}$
• C. $\frac{5}{13}$
• D. $\frac{6}{13}$

Answer 1

The correct option is B $\frac{24}{65}$

Probability of getting black shoes $=\frac{2}{5}$

Probability of getting brown shoes $=\frac{3}{5}$

Probability of getting black socks $=\frac{6}{13}$

Probability of getting brown socks $=\frac{4}{13}$

Probability of getting same colour of socks and shoes $=$black shoes $\times$ blackl socks $+$ brown shoes$\times$brown socks

$=\frac{2}{5}\times \frac{6}{13}+\frac{3}{5}\times \frac{4}{13}=\frac{24}{65}$