Suppose that the proportions of blood phenotypes in a partic

Suppose that the proportions of blood phenotypes in a particular population are as follows:

Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? (Enter your answer to four decimal places.)


What is the probability that the phenotypes of two randomly selected individuals match? (Enter your answer to four decimal places.)

Solution

A. what is the probability that both phenotypes are O?

The proportions all add up to 1 as expected, so the probability that a randomly selected person has blood type O is 0.41. So the probability that the first person is O and the second person is O too is 0.41 * 0.41 = 0.1681
The probability that both phenotypes are O is 0.1681.

B. What is the probability that the phenotypes of two randomly selected individuals match

To find the probability that two people are a \"match\", you need to find this:
P( two people are A, OR the two people are B, OR the two people are AB, OR the two people are O) =
P(two people are A) + P(two people are B) + P(two people are AB) + P(two people are O)
=(0.50)^2 + (0.07)^2 + (0.02)^2 + (0.41)^2=.4234

the probability that the phenotypes of two randomly selected individuals match 0.4234.