Answer to Question #146222 in Statistics and Probability for Jocelyn

Question

Probability that none of five people blood is type b out of 11%

Answer 1

The probability that a person has type B is 11 %. Five unrelated people are selected at random. Find the probability that none of the five have type blood.

A = person has blood type B

C = none of the five people have blood type B

The probability that a person has type B is 11 %:

P(A) = 11 % = 0.11

Use the complement rule to determine the probability that a person does not have blood type B:

P(A’) = 1 – P(A) = 1 – 0.11 = 0.89

Since the adults are randomly selected, it is safe to assume that the blood type of the five people are independent and thus we can use the multiplication rule for independent events:

$P(C) = P(A’) \times P(A’) \times P(A’) \times P(A’) \times P(A’) = (P(A’))^5 = 0.89^5 = 0.5584$

Answer: 0.5584