Question

Approximately 26% of people have Rh negative blood. We will check the blood tests of the next 12 people to enter an emergency clinic with injuries that may require transfusion. Assume no two belong to the same family.

a) What is the probability that exactly 5 of those patients will have Rh negative blood?

b) What is the probability that at least 3 of them will have Rh negative blood?

c) What are the expected number and standard deviation of the number of these patients with Rh negative blood?

Answer 1

Explanation:

Let X be the number of persons out of 12 who have RH negative blood.

X is binomial since each person is independent of the other to have Rh negative blood.

n =12

a) What is the probability that exactly 5 of those patients will have Rh negative blood?

P(X=5) =
`12C5 (0.26)^5 (1-0.26)^7\\= 0.1143`

b) What is the probability that at least 3 of them will have Rh negative blood?

`P(X\geq 3) = \Sigma_3^(12) 12Cr (0.26)^r (1-0.26)^(12-r)`=0.6397

c) What are the expected number and standard deviation of the number of these patients with Rh negative blood?

E(X) = np =
`12(0.26) = 3.12`

Var(x) = npq =
`3.12 *0.74`

Std dev =
`√(Varx) \\=1.5195`