Question

Suppose that the proportions of blood phenotypes in a particular population are as follows: A B AB O 0.48 0.13 0.03 0.36 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.)

Answer 1

Answer:

P(O and O) =0.1296

P=0.3778

Step-by-step explanation:

Given that

blood phenotypes in a particular population

A=0.48

B=0.13

AB=0.03

O=0.36

As we know that when A and B both are independent that

P(A and B)= P(A) X P(B)

The probability that both phenotypes O are in independent:

P(O and O)= P(O) X P(O)

P(O and O)= 0.36 X 0.36 =0.1296

P(O and O) =0.1296

The probability that the phenotypes of two randomly selected individuals match:

Here  four case are possible

So

P=P(A and A)+P(B and B)+P(AB and AB)+P(O and O)

P=0.48 x 0.48 + 0.13 x 0.13 + 0.03 x 0.03 + 0.36 x 0.36

P=0.3778

Answer 2

P(O and O) =0.1296

P=0.3778

• The calculation is as follows:

The independent case is

$P(A and B)= P(A) \times P(B)$

The probability that both phenotypes O are in independent is

$P(O and O)= P(O) \times P(O)\\\\P(O and O)= 0.36 \times 0.36 =0.1296$

P(O and O) =0.1296

So

P=P(A and A)+P(B and B)+P(AB and AB)+P(O and O)

$P=0.48 \times 0.48 + 0.13 \times 0.13 + 0.03 \times 0.03 + 0.36 \times 0.36$

P=0.3778

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