Multiple choice

A bag contains $3$ red, $4$ white and $5$ blue balls. If two balls are drawn at random, then the probability that they are of different colours, is

  1. $\cfrac { 47 }{ 66 } $
  2. $\cfrac { 23 }{ 33 } $
  3. $\cfrac { 47 }{ 132 } $
  4. $\cfrac { 47 }{ 33 } $
  5. $\cfrac { 70 }{ 33 } $
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A Correct answer
Explanation

Total balls = 12. Total ways to pick 2 = 12C2 = 66. Ways to pick same color: (3C2 + 4C2 + 5C2) = 3 + 6 + 10 = 19. Ways to pick different colors = 66 - 19 = 47. Probability = 47/66.

AI explanation

The bag contains 12 balls total, so the number of ways to draw any 2 balls is 12C2, which equals 66. The favorable outcomes of drawing different colours are calculated by adding the products of each pair: (3 times 4) plus (3 times 5) plus (4 times 5), giving 12 plus 15 plus 20, for a total of 47. The probability is 47 divided by 66.