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Four persons independently solve a certain problem correctly with probabilities (1)/(2), (3)/(4), (1)/(4), (1)/(8). Then the probability that the problem is solved correctly by at least one of them is -

1. (235)/(256)
2. (21)/(256)
3. (3)/(256)
4. (253)/(256)

Correct answer: (235)/(256)

Solution

The probability of at least one person solving the problem is 1 minus the probability that none solve it. Calculating this gives 1 - (1/2 × 1/4 × 3/4 × 7/8) = 235/256.

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