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Solve the following.
Three persons A, B and C shoot to hit a target. Their probabilities of hitting the target are , and…
Three persons A, B and C shoot to hit a target. Their probabilities of hitting the target are $\dfrac{5}{6}$, $\dfrac{4}{5}$ and $\dfrac{3}{4}$ respectively. Find the probability that:
Exactly two persons hit the target.
Answer
Answer
AI$P(A) = \frac{5}{6}$, $P(B) = \frac{4}{5}$, $P(C) = \frac{3}{4}$, so $P(A') = \frac{1}{6}$, $P(B') = \frac{1}{5}$, $P(C') = \frac{1}{4}$.
$P(\text{exactly two}) = P(A)P(B)P(C') + P(A)P(B')P(C) + P(A')P(B)P(C)$
$= \frac{5}{6}\cdot\frac{4}{5}\cdot\frac{1}{4} + \frac{5}{6}\cdot\frac{1}{5}\cdot\frac{3}{4} + \frac{1}{6}\cdot\frac{4}{5}\cdot\frac{3}{4} = \frac{20 + 15 + 12}{120}$
Final answer: $\frac{47}{120}$
From ISC 2020 Mathematics Paper 1, question 10(i).