Some traits of plants and animals depend on inheritance of a single gene. This i

Question

Some traits of plants and animals depend on inheritance of a single gene. This is called Mendelian inheritance, after Gregor Mendel (1822-1884). Each of us has an ABO blood type, which describes whether two characteristics, called A and B, are present. Every one of us has two blood type alleles (gene forms), one inherited from our mother and one from our father. Each of these alleles can be A, B, or O. Which two we inherit determines our blood type. Here is a table that shows what our blood type is for each combination of two alleles.

We inherit each of a parent's two alleles with probability 0.5. We inherit independently from our mother and father.

Samantha has alleles B and O. Dylan has alleles A and B. They have two children. What is the probability that both children have blood type A? (Round your answer to three decimal places.)

What is the probability that both children have different blood types?

Alleles inherited Blood type A and A A A and B AB A and O A B and B B B and O B O and O O

Explanation / Answer

Solution:-

Step1:

One half of the parents alleles are O, one quarter are A, and the other quarter are B.

Therefore, P(O)=0.5, P(A)=0.25, and P(B)=0.25.

P(Blood Type=O) = P(genotype=OO) = P(O)² = 0.5² = 0.25

The probability that a child of these parents has blood type O is 0.25

Step2:

Using the multiplication rule for independent events,

P(OO) = P(OO)³ = 0.25³ = 1/64 = 0.015625

The probability that all three have blood type O is:0.015625

Step3:

Probability of not getting blood type 0 is,

P(not OO) = 1 P(OO) = 1 0.25 = 0.75

P(OO and not OO) = P(OO)P(not OO)² = 0.25 0.75² = 0.141

The probability that the first child has blood type O and the next two do not is: 0.141

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