Question

According to insurance records a car with a certain protection system will be recovered 8787​% of the time. find the probability that exactly 55 of 1010 stolen cars will be recovered. round to the nearest thousandth.

Answer 1

Let X be the number of cars recovered from stolen cars. Let n be the total number of stolen cars and p be the probability that car will be recovered.

Given: n=10, x=5

It is given that a car with a certain protection system will be recovered 87​% of the time. It means probability of recovering a car is p=0.87

Probability that 5 out of 10 stolen cars will be recovered is

P(X=x ) = $nCx p^{x} (1-p) ^{n-x}$

P(X=5) = $10C5 0.87^{5} (1-0.87) ^{10-5}$

P(X=5) = 0.0047

The probability that exactly 5 out of 10 stolen cars will be recovered is 0.0047