Question

4.40 Two children.

Each of us has an ABO blood type, which describes whether two characteristic, 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 inherited alleles:

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

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? (report to 4 decimal places as a proportion) ________________________

What is the probability that both children will have the same blood type? (report to 3 decimal places as a proportion) _________________

Answer 1

answer:

given that Samantha has alleles B and O , and Dylan has alleles A and B

and we can observe that getting B and O and are mutually disjoint events also getting A and B also mutually disjoint events.

1) probability of the both children having blood type A

= (probability of 1st child having blood type A)(probability of 2nd child having blood type A)

= {(probability of getting O from Samantha)(probability of getting A from Dylan)} x

   {(probability of getting O from Samantha)(probability of getting A from Dylan)}

#since probability of getting O from Samantha and probability of getting A from Dylan are independent events.

   =(0.5)(0.5)(0.5)(0.5)

= 0.0625

2)

There is only two possibilities for both children will have the same blood type

i.e., i) both children having A blood group by receiving O from Samantha and A from Dylan,

ii) both children having B blood group by receiving B or O from Samantha and B from Dylan.

for our convenience let the case (i) = M and case (ii) = N.

therefore,

probability that both children having the same blood type = M+N

from the problem (1) we have M=0.0625

now let us find N,

N = (probability of 1st child having blood type B)(probability of 2nd child having blood type B)

= {(probability of getting B or O from Samantha)(probability of getting B from Dylan)} x

{(probability of getting B or O from Samantha)(probability of getting B from Dylan)}

#since probability of getting B or O from Samantha and probability of getting B from Dylan are independent events.

= (1)(0.5)(1)(0.5)

#since Samantha gave B and O alleles , hence the event getting B or O is a sure event with probability 1

= 0.25

therefore ,

probability that both children having the same blood type = M+N

= 0.0625 + 0.25

= 0.3125

Thank you.