Multiple choice

A bag contains 12 balls, of which 3 are red, and 5 balls are drawn at random. Find the probability that 5 balls 3 are red.

  1. 3/132

  2. 5/396

  3. 1/36

  4. 1/22
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To get exactly 3 red balls, all 3 red balls must be selected and 2 of the 9 non-red balls must be selected. The probability is C(3,3) × C(9,2) / C(12,5) = 36/792 = 1/22.

AI explanation

Assuming the question intends for exactly 3 red balls to be drawn from a bag of 12 containing 3 red balls, we calculate the probability using combinations. The total ways to draw 5 balls from 12 is the combination of 12 taken 5 at a time, which equals 792. The number of ways to choose exactly 3 red balls from the 3 available multiplied by the number of ways to choose the remaining 2 balls from the 9 non-red balls is 1 multiplied by the combination of 9 taken 2 at a time, which is 36. The probability is 36 divided by 792, which simplifies to 1 divided by 22. If the question implies drawing all 3 red balls, the answer remains 1 divided by 22.

Keep practicing — related questions