Independence of complements. Show that if events A and B obey the multiplication rule, P(A and B) = P(A)P(B), then A and the complement Bc of B also obey the multiplication rule, P(A and Bc) = P(A)P(Bc). That is, if events A and B are independent, then A and Bc are also independent.
Mendelian inheritance. Some traits of plants and animals depend on inheritance of a single gene. This is called Mendelian inheritance, after Gregor Mendel (1822-1884). Exercises 5.36 to 5.39 are based on the following:
Each of us has an ABO blood type, which describes whether two characteristics called A and B are present. Every human being 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:
|
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 our father.