Paragraph: A box $B_{1}$ contains $1$ white ball, $3$ red balls and $2$ black balls. Another box $B_{2}$…

Paragraph: 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.
Question: 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
  1. 8 2 6 4 8
  2. 9 0 6 4 8
  3. 5 5 8 6 4 8
  4. 5 6 6 6 4 8

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

Asked in: JEE Advanced 2013 (Paper 2)

Practice more Probability questions on Aicharya