A problem is given to three students whose individual probabilities of solving it are 1/2, 1/3 and 1/4. If all three attempt it independently, what is the probability that the problem gets solved?

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Accepted Answer

3/4. 'Solved' means at least one succeeds, so use the complement. P(none solves) = (1 - 1/2)(1 - 1/3)(1 - 1/4) = 1/2 x 2/3 x 3/4 = 1/4. Hence P(solved) = 1 - 1/4 = 3/4. The value 1/24 is the probability that all three solve it.

A problem is given to three students whose individual probabilities of solving it are 1/2, 1/3 and 1/4. If all three attempt it independently, what is the probability that the problem gets solved?

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