Multiple choice

A bag contains 3 white balls, 4 green balls and 5 red balls. Three balls are drawn from the bag without replacement, find the probability that the balls are all the same color.

  1. $\dfrac{1}{99}$
  2. $\dfrac{1}{22}$
  3. $\dfrac{1}{34}$
  4. $\dfrac{3}{44}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 3+4+5 = 12. Probability of drawing 3 white balls = (3/12)(2/11)(1/10) = 6/1320. Probability of 3 green = (4/12)(3/11)(2/10) = 24/1320. Probability of 3 red = (5/12)(4/11)(3/10) = 60/1320. Sum = (6+24+60)/1320 = 90/1320 = 9/132 = 3/44.

AI explanation

The total number of balls is 12, and the total ways to draw three balls is 12C3, which equals 220. The favorable outcomes are drawing three white balls, three green balls, or three red balls, calculated as 3C3 + 4C3 + 5C3, which is 1 + 4 + 10 = 15. The probability is the ratio of favorable outcomes to total outcomes, which is 15/220. Simplifying this fraction yields 3/44.

Keep practicing — related questions