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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?
Answer & Solution
Correct Answer:
Option
A
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 $$ = \frac{1}{{105}} + \frac{1}{{35}} = \frac{4}{{105}}$$
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 $$ = \frac{1}{{105}} + \frac{1}{{35}} = \frac{4}{{105}}$$
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