JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · Probability XII

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 balls, 4 red balls and 5 black balls.

If 1 ball is drawn from each of the boxes

B_{1}, B_{2}

and

B_{3}

, the probability that all 3 drawn balls are of the same colour is

Answer: (A)

Solution

The probability that all three balls are of the same color is:

P (all white) + P (all red) + P (all black)

P (all white) = \frac{1}{6} \times \frac{2}{9} \times \frac{3}{12} = \frac{6}{648}

P (all red) = \frac{3}{6} \times \frac{3}{9} \times \frac{4}{12} = \frac{36}{648}

P (all black) = \frac{2}{6} \times \frac{4}{9} \times \frac{5}{12} = \frac{40}{648}

Total probability =

\frac{6 + 36 + 40}{648} = \frac{82}{648}

JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · Single correct option