An Olympic archer is able to hit the bull’s eye 75% of the time. Assume each...

An Olympic archer is able to hit the bull’s eye 75% of the time. Assume each shot is independent of the others. If she shoots 5 arrows, what’s the probability that she gets at least 4 bull’s eyes? Give your answer to 3 decimal places.

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Expert Solution

It is given that the An Olympic archer is able to hit the bull’s eye 75% of the time it means the probability that she hit the bull's eye is p=75%=0.75

She shots 5 arrows i.e. n=5 and each shot is independent of the others.

So, if we denote the no. of bull's eyes by X. Then, it is clear that X~B(n=5,p=0.75)

We have to find the probability that she gets at least 4 bull’s eyes i.e. P(X≥4) = P(X=4)+ P(X=5)

; x=0,1,2,…..n

Hence, the probability that she gets at least 4 bull’s eyes is 0.632

orchestra answered 1 year ago

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