Question

According to police sources, a car with a certain protection system will be recovered 87% of the time. Find the probability that 4 of 8 stolen cars will be recovered?

Answer 1

Answer: 0.01145

Explanation:

We use Binomial distribution , where the probability of getting x successes in n trial is given by :-

`P(x)=^nC_xp^x(1-p)^(n-x)` , p = probability of getting each success in each trial.

As per given

The proportion that a car with a certain protection system will be recovered= p=0.87

n= 8

Let x be the number of cars will be recovered.

Then, the probability that 4 of 8 stolen cars will be recovered:

`P(X=4)=^8C_4(0.87)^4(1-0.87)^(8-4)`

`=(8!)/(4!(8-4)!)(0.87)^4(0.13)^4\\\\= 70(0.57289761)(0.00028561)\\\\=0.0114537700474\approx0.01145`

Hence, the required probability is 0.01145.