The four major blood types are present in approximately the following proportions in the population of the U.S.A.
|
Type
|
A
|
B
|
AB
|
0
|
|
Proportion
|
42%
|
10%
|
4%
|
44%
|
Note that each person's blood is exactly one of these four types. Type AB is a separate type, not the intersection of type A and type B,
a) If two people are picked at random from this population, what is the chance that their blood is of the same type? Of different type?
b) If four people are picked at random, let P(k) be the chance that there are exactly k different blood types among them. Find P(k) for k = 1, 2, 3, 4,.