Suppose that lesions are present at 5 sites among 50 in a patient. A biopsy selects 8 sites randomly (without replacement).

(a) What is the probability that lesions are present in at least one selected site?

(b) What is the probability that lesions are present in two or more selected sites?

(c) Instead of eight sites, what is the minimum number of sites that need to be selected to meet the following objective? The probability that at least one site has lesions present is greater than or equal to 0.9.

Step 1 of 4:

The lesions are present at 5 sites among 50 in a patient.

A biopsy selects 8 sites randomly without replacement.

We have to find the probability that lesions are present in at least one selected site.We have to find the probability that lesions are present in two or more selected sites.We have to find the minimum number of sites that need to be selected to meet the object that the probability that at least one site has lesions present is greater than or equal to 0.9.Step 2 of 4:

Let X be the number of lesions in patients.

Given population size, N= 50.

Sample, n = 8.

The number of patients that lesions are present in the population, K= 5.

From the given information, it is clear that X~ Hypergeometric distribution.

P(X=k) = x[ 0, n+K-N,..., ,min(n,K)]

P(X=k) =

(a)

The probability that lesions are present in at least one selected site.

P(X) = 1- P(X=0)

= 1-

= 1-

= 1- 0.4014

= 0.5986

Therefore, the probability that lesions are present in at least one selected site is 0.5986.