Paragraph: A box B₁ contains 1 white ball, 3 red balls and 2 black balls. Another box B₂ contains 2 white balls, 3 red balls and 4 black balls. A third box B₃ contains 3 white balls, 4 red balls and 5 black balls. Question: If 1 ball is drawn from each of the boxes B₁, B₂ and B₃ , the probability that all 3 drawn balls are of the same colour is

Step-by-step solution

P ( W   W   W )   +   P   ( R   R   R )   +   P ( B   B   B ) 1 6 × 2 9 × 3 1 2 + 3 6 × 3 9 × 4 1 2 + 2 6 × 4 9 × 5 1 2 ⇒      6 + 3 6 + 4 0 6 × 9 × 1 2      ⇒     8 2 6 4 8