Question

A bag contains $5$ black and $6$ white balls. If two balls are drawn together at random, then the probability that these being of different colour

• A. $\frac{5}{11}$
• B. $\frac{6}{11}$
• C. $\frac{11}{6}$
• D. $\frac{6}{16}$

Answer 1

Answer: (B)

$\frac{6}{11}$

Probability $=\frac{Favorablecase}{samplespace}$

Probability of both balls being black =

$\frac{5}{11}\times \frac{4}{10}=\frac{2}{11}$

Probability of both balls being white =

$\frac{6}{11}\times \frac{5}{10}=\frac{3}{11}$

Probability of both balls being of same

colour $=\frac{2}{11}+\frac{3}{11}=\frac{5}{11}$

So, Probability of both balls being different

in colour $=1-\frac{5}{11}=\frac{6}{11}$