Question

A box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_3$ contains 3 white ball, 4 red balls and 5 black balls. If one ball is drawn from each of the boxes $B_1,B_2$ and $B_3$, the probability that all three drawn balls are of the same colour is

• A. $\frac{82}{648}$
• B. $\frac{90}{648}$
• C. $\frac{558}{648}$
• D. $\frac{566}{648}$

Answer 1

The correct option is A $\frac{82}{648}$

Probability that all the balls drawn are white is $\frac{1}{6}\times \frac{2}{9}\times \frac{3}{12}$
Probability that all the balls drawn are red is $\frac{3}{6}\times \frac{3}{9}\times \frac{4}{12}$
Probability that all the balls drawn are blue is $\frac{2}{6}\times \frac{4}{9}\times \frac{5}{12}$
Therefore, the probaility that all the balls drawn are of same colour is $\frac{6}{648}+\frac{36}{648}+\frac{40}{648}=\frac{82}{648}$