Question

BASED ON A TRUE STORY: In Costa Rica there are howling monkeys living on mango trees. People sometimes annoy them and they will throw mangoes at the people. 5 tourists arrive in a car and start harassing the monkeys. The monkeys attack the tourists by throwing mangoes. Assume each attack on a tourist is independent and that in every attempt there is a 0.15 chance that the monkey will hit a tourist.

Find the probability of hitting more than 1 but no more than 3 tourists.

Answer 1

No. of tourists, n = 5

The probability that the monkey will hit a tourist, p = 0.15

The probability that the monkey will not hit a tourist, q (1-p) = 0.85

This is a binomial distribution with n=5, p=0.15 and q=0.85

Let X be the binomial random variable indicating the required probability

P(X=x) =C(n,x)*(p)^x*(q)^n-x

P(1<X<=3) = P(X=2) + P(X=3)

P(X=2) = C(5,2)*(0.15)^2*(0.85)^3 = 0.138

P(X=3) = C(5,3)*(0.15)^3*(0.85)^2 = 0.024

P(1<X<=3) = 0.138+0.024 = 0.162

Required Probability = 0.162

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Probability that the monkey will hit a tourist, p = 0.15