Multiple choice

A bag contain $7$ white, $5$ black and $4$ red balls. If two balls are drawn at random, find the probability that one ball is black and the other red

  1. $\dfrac {5}{6}$
  2. $\dfrac {2}{6}$
  3. $\dfrac {1}{6}$
  4. $\dfrac {5}{12}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 7+5+4 = 16. Ways to choose 2 balls = 16C2 = (16*15)/2 = 120. Ways to choose 1 black and 1 red = 5C1 * 4C1 = 20. Probability = 20/120 = 1/6.

AI explanation

The total number of balls in the bag is 7 white + 5 black + 4 red = 16 balls. The total number of ways to draw 2 balls is 16C2, which equals 120. The number of ways to draw 1 black ball from 5 and 1 red ball from 4 is 5C1 times 4C1, giving 5 times 4 = 20 favorable combinations. Therefore, the required probability is 20 divided by 120, which simplifies to 1/6.

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