CA Foundation · Quantitative Aptitude · Probability
Four letters are written and placed at random, one in each of four addressed envelopes, in one-to-one fashion. What is the probability that none of the letters is placed in its correct envelope?
The probability is 3/8. Of the 24 possible ways of placing four letters in four envelopes, exactly 9 are derangements where no letter reaches its own envelope, so the probability is 9/24, which simplifies to 3/8.
- A3/8Correct
- B1/3
- C1/4
- D5/12
Explanation
Total arrangements = 4! = 24. Derangements of 4 objects = 24(1 - 1 + 1/2 - 1/6 + 1/24) = 9. Probability = 9/24 = 3/8. The option 1/3 comes from using the derangement count 8 instead of 9.
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