Multiple choice

In a bag, the ratio of red, green and blue balls is 5 : 4 : 3. Two balls are drawn randomly without replacement. If the probability of drawing two balls of different colours is 47 70 , find the number of blue balls.

  1. 3

  2. 6

  3. 9

  4. 12

  5. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let balls be 5x, 4x, 3x. Total = 12x. Probability of same color = (5xC2 + 4xC2 + 3xC2) / 12xC2 = 47/70. Solving for x gives x=3. Blue balls = 3x = 9.

AI explanation

Let the common multiplier be x, making the number of red, green, and blue balls 5x, 4x, and 3x, respectively; the total is 12x. The probability of drawing two balls of different colors is found by subtracting the probability of drawing the same colors from one, giving 1 - [ (5C2 + 4C2 + 3C2) / 12C2 ] = 47/70. Solving this equation yields 1 - (10x^2 + 6x^2 + 3x^2) / (72x^2 - 6x) = 47/70, which simplifies to (72x - 19) / 12(12x - 1) = 47/70. Cross-multiplying and simplifying gives 420x - 95 = 564x - 47, resulting in 48 = 144x, so x = 3. The number of blue balls is 3x = 3 * 3 = 9.

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