Question

1. Use the data in the following table, which summarizes blood groups and Rh types for typical people. These values may vary in different regions according to the ethnicity of the population. Group AB Type Rh+ 「39 31 10 a If one person is randomly selected, find the probability of getting someone who is not group A. b. If one person is randomly selected, find the probability of getting someone who is group A or type Rh Find the probability that he or she had Rh+ given that the subject was blood type O. Are the events " had Rh+ "and " blood type O " independent? Use the definition of independence and probabilities to justify your answer to this question. c. d. e. What is the probability of having blood type A or B, given that the type is Rh+? f. If two different subiects are randomly selected, find the probability that they both blood type AB.

Answer 1

From the given data, the following Table is calculated:

	O	A	B	AB	Total
RH+	39	31	8	9	87
RH-	5	10	9	6	30
Total	44	41	17	15	117

(a)
P(Not A) = 1 - P(A) = 1 - (41/117) = 1 - 0.3504 = 0.6496

(b)

P(A OR RH-) = P(A) + P(RH-) - P(A AND RH-)

                  = (41/117) + (30/117) - (10/117)

                      = 61/117 = 0.5214

(c)
P(RH+/O) = P(RH+ AND O)/P(O)

               = 39/44 = 0.8864

(d)

P(RH+ AND O) = 39/117 = 0.3333

P(RH+) = 87/117 = 0.7436

P(O) = 44/117 = 0.3761

P(RH+) X P(O) = 0.2796

Since P(RH+ AND O) $\neq$ P(RH+) X P(O), we conclude that the events"had Rh +" and "blood type O" are not independent.

(e)

P(A OR B/RH+) = P(A OR B AND RH+)/P(RH+)

                        = 39/87 = 0.4483

(f)

P(Two subjects AB) = (15/117)² = 0.0164