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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:
At least one person hits the target.
Answer
Answer
AI$P(\text{at least one}) = 1 - P(\text{none hits}) = 1 - P(A')P(B')P(C')$
$= 1 - \frac{1}{6}\cdot\frac{1}{5}\cdot\frac{1}{4} = 1 - \frac{1}{120}$
Final answer: $\frac{119}{120}$
From ISC 2020 Mathematics Paper 1, question 10(ii).