JEE Advanced · 2013 · 02 Jun 2013 · Paper 1 · Probability XII

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 at least one of them is

(A) $\frac{235}{256}$ ✓ Correct
(B) $\frac{21}{256}$
(C) $\frac{3}{256}$
(D) $\frac{253}{256}$

Answer: (A)

Solution

The probability that none of them solves the problem is the product of their failure probabilities:

P (none) = (1 - \frac{1}{2}) (1 - \frac{3}{4}) (1 - \frac{1}{4}) (1 - \frac{1}{8}) = \frac{1}{2} \times \frac{1}{4} \times \frac{3}{4} \times \frac{7}{8} = \frac{21}{256}

. Therefore, the probability that at least one solves it is

P (at least one) = 1 - \frac{21}{256} = \frac{235}{256}

JEE Advanced · 2013 · 02 Jun 2013 · Paper 1 · Single correct option

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