CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
In a godown of Sharma Traders, 12 of 20 sacks contain rice and the rest contain wheat. Two sacks are drawn one after another without replacement. What is the probability that both contain rice?
The probability is 33/95. The first sack is rice with probability 12/20, and given that, the second is rice with probability 11/19 because there is no replacement. Multiplying gives 132/380, which simplifies to 33/95.
- A33/95Correct
- B9/25
- C3/5
- D11/20
Explanation
P(first rice) = 12/20. P(second rice | first rice) = 11/19. Product = (12×11)/(20×19) = 132/380 = 33/95. The option 9/25 comes from wrongly treating the draws as with replacement (0.6×0.6 = 9/25 would be 0.36 vs 0.347).
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