Multiple choice

A bag contains x green balls, 7 blue balls and 8 red balls. When two balls are drawn from bag randomly, then the probability of one ball being green and one ball being red is 4/15. Find value of x (number of green balls cannot be more than 18 balls).

  1. 3

  2. 5

  3. 10

  4. 9

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

Total balls = x + 15. Probability of one green and one red is [xC1 * 8C1] / [(x+15)C2] = 4/15. This simplifies to 8x / [((x+15)(x+14))/2] = 4/15, or 16x / (x^2 + 29x + 210) = 4/15. Solving 60x = x^2 + 29x + 210 gives x^2 - 31x + 210 = 0, which factors to (x-10)(x-21) = 0. Given x <= 18, x = 10.

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