Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/8 respectively. If all hit at the target independently, then the probability that the target would be hit, is

Four persons can hit a target correctly with probabilities… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 9 Apr · Shift II

Four persons can hit a target correctly with probabilities

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

and

\frac{1}{8}

respectively. If all hit at the target independently, then the probability that the target would be hit, is

Show answer and solution

Correct option: B

Solution

P(target is hit) = 1 - P(none hits) = 1 - (1 - 1/2)(1 - 1/3)(1 - 1/4)(1 - 1/8) = 1 - (1/2)(2/3)(3/4)(7/8) = 1 - 42/192 = 1 - 7/32 = 25/32.

[JEE Main 2019 · 9 Apr · Shift II]

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