Problem 61E

Of the volunteers donating blood in a clinic, 80% have the Rhesus (Rh) factor present in their blood.

a If five volunteers are randomly selected, what is the probability that at least one does not have the Rh factor?

b If five volunteers are randomly selected, what is the probability that at most four have the Rh factor?

c What is the smallest number of volunteers who must be selected if we want to be at least 90% certain that we obtain at least five donors with the Rh factor?

Solution :

Step 1 of 3:

Given the Rhesus factor present in their blood is 80%.

Our goal is:

a). We need to find the probability that at least one does not have the Rh factor.

b). We need to find the probability that at most four have the Rh factor.

c). We need to find the smallest number of volunteers who must be selected.

a).

Given if 5 volunteers are selected randomly, then we have to find the probability that at least one does not have the Rh factor.

We know that the probability that volunteer have Rh factor is 0.8.

X is not having Rh factor.

P(X1)=1-P(X<1)

P(X1)=1-P(X=0)

The formula of the binomial distribution is

P(X) = ;

Given n=5, p=0.2

Then,

P(X1)=1-P(X=0)

P(X1)=1-

P(X1)=1-

P(X1)=1-

P(X1)=0.67232

Therefore, the probability that at least one does not have the Rh factor is 0.67232.