Blood Type About 45 % of the populations of the United States and Canada have Type O blood.

(a) If a random sample of ten people is selected, what is the probability that exactly five have Type O blood?

(b) What is the probability that at least three of the random sample of ten have Type O blood?

(a)

To find:

The probability that exactly five have Type O blood in a random sample of ten people.

Given:

45% of the populations of the United States and Canada have Type O blood.

Approach:

For a binomial experiment with two outcomes with outcome of success in each trial equal to p.

The probability of r successes in n trials is equal to

P (r successes in n trials) =C(n,r)pr(1−p)n−r (1)

Calculation:

Interpret this problem as a binomial experiment with two outcomes: a person has Type O blood or the person does not have Type O blood. “Success” is the event that a person has Type O.

Probability of success,

p=0.45

Number of trials, n=10

Problem asks probability of exactly five people having Type O blood. This gives:

r=5

Substitute n,p,r in equation (1) to get

(b)

To find:

The probability that at least three have Type O blood in a random sample of ten people.