JEE PYQ: Probability Question 34
Question 34 - 2019 (09 Apr Shift 1)
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:
(1) $\frac{25}{192}$
(2) $\frac{7}{32}$
(3) $\frac{1}{192}$
(4) $\frac{25}{32}$
Show Answer
Answer: (4)
Solution
$P(\text{hit}) = 1 - P(\text{all miss}) = 1 - \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{7}{8} = 1 - \frac{42}{192} = 1 - \frac{7}{32} = \frac{25}{32}$.
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