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Sam can hit a target 1 time in 4 shots, Jack can hit the target 2 times in 4 shots and Raj can hit the target 6 times in 6 shots. What is the probability that at least 2 shots hit the target?

Solution

✅ Correct Option: 3
PersonGivenHitsMisses
Sam1 in 4 shots14\dfrac{1}{4}34\dfrac{3}{4}
Jack2 in 4 shots24=12\dfrac{2}{4}=\dfrac{1}{2}12\dfrac{1}{2}
Raj6 in 6 shots66=1\dfrac{6}{6}=100

Raj never misses, so one hit is already guaranteed. To get at least 2 hits we only need at least one hit from Sam or Jack.


It is quicker to find the opposite case, where both of them miss.

P(both miss)=34×12=38P(\text{both miss})=\dfrac{3}{4}\times\dfrac{1}{2}=\dfrac{3}{8}


P(at least 2 hits)=1−38=58P(\text{at least 2 hits})=1-\dfrac{3}{8}=\dfrac{5}{8}

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