JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Probability

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:

Answer: (A)

Solution

The target is hit unless everyone misses. The misses have probabilities

\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{7}{8}

, and multiplying,

P (all miss) = \frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdot \frac{7}{8} = \frac{7}{32}

. So the chance of a hit is

1 - \frac{7}{32} = \frac{25}{32}

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option