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 atleast one of them, is

Four persons independently solve a certain problem… — JEE Main 2013 Mathematics PYQ

JEE Main 2013

Four persons independently solve a certain problem correctly with probabilities

\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}

. Then, the probability that the problem is solved correctly by atleast one of them, is

Show answer and solution

Correct option: A

Solution

P(none solves) = (1 - 1/2)(1 - 3/4)(1 - 1/4)(1 - 1/8) = (1/2)(1/4)(3/4)(7/8) = 21/256.

P(at least one solves) = 1 - 21/256 = 235/256.

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