Question

1. The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and 4% Type AB. Suppose we select 5 blood donors at random.
   1. What is the probability that the fifth donor is the first donor with Type O blood?
   2. What is the probability exactly two of the five donors will have Type O blood?
   3. What is the probability none of the five donors will have Type O blood?
   4. What is the probability at least one of the five donors will have Type O blood?

Answer 1

Pr(O Population) = 0.45

P(Type A) = 0.40

P(Type B) = 0.11

P(Type AB) = 0.04

Total 5 blood donors were at random.

(a) We have to find that the fifth donor is the first donor with type O blood. That means starting four donors are not type O blood and fifth one is type O blood.

P(Fifth donor is the first donor with type O blood) = (1 - 0.45)⁴ * 0.45 = 0.0412

(b) P(Exactly two of the five donors have type O blood) = ⁵C₂ (0.45)² (0.55)³ = 0.3369

(c) P(None of the donors have type O blood) = ⁵C₀ (0.55)⁵ = 0.0503

(d) P(at least one of the five donors have type O blood) = 1 - P(None have type O blood) = 1 - 0.0503 = 0.9497