A box has 6 black, 4 red, 2 white and 3 blue shirts. When 2 shirts are picked randomly, what is the probability that either both are white or both are blue?

A. $$\frac{{4}}{{105}}$$

B. $$\frac{{1}}{{35}}$$

C. $$\frac{{1}}{{105}}$$

D. $$\frac{{1}}{{15}}$$

Answer: Option A

Solution(By Examveda Team)

Both white or both blue
Total shirts = 15
There are 2 white and 3 blue shirts
Probability for 2 white shirts $$ = \frac{2}{{15}} \times \frac{1}{{14}} = \frac{1}{{105}}$$
Probability for 2 blue shirts $$ = \frac{3}{{15}} \times \frac{2}{{14}} = \frac{1}{{35}}$$
Total Probability $$ = \frac{1}{{105}} + \frac{1}{{35}} = \frac{4}{{105}}$$