CA Foundation · Quantitative Aptitude · Probability
A box holds 5 red and 4 white balls. Three balls are drawn at random one after another without replacement. What is the probability that exactly 2 of them are red?
The probability is 10/21. Choosing 3 balls from 9 can be done in 84 ways. Choosing 2 red from 5 and 1 white from 4 can be done in 10 times 4, which is 40 ways. Hence 40 divided by 84 simplifies to 10/21.
- A10/21Correct
- B100/243
- C5/21
- D4/9
Explanation
Total ways to choose 3 of 9 balls = C(9,3) = 84. Favourable ways = C(5,2) x C(4,1) = 10 x 4 = 40. The probability is 40/84 = 10/21. The option 100/243 results from wrongly treating the draws as with replacement.
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