Question

Two balls are drawn from a bag containing $5$ white and $7$ black balls at random. What is the probability that they would be of different colours?

• A. $\frac{35}{66}$
• B. $\frac{30}{66}$
• C. $\frac{12}{66}$
• D. None of above

Answer 1

Answer: (A)

$\frac{35}{66}$

A bag contains $5$ white and $7$ black balls.

Probability of drawing $2$ balls of different colour

$\Rightarrow \frac{{}^5{C}_1\times {}^7{C}_1}{{}^{12}{C}_2}=\frac{5\times 7}{66}=\frac{35}{66}$

Hence, the answer is $\frac{35}{66}.$