4.47 Consider an experiment, the events A and B, and probabilities P(A) 5 0.55, P(B) 5 0.45, and P(A d B) 5 0.15. Find the probability of: a. A or B occurring. b. A and B occurring. c. Just A occurring. d. Just A or just B occurring.

a) 0.85

b) 0.15

c) 0.40

d) 0.70

Step-by-step explanation:

P(A) = 0.55

P(B) = 0.45

P(A n B) = 0.15

a) Probability of A or B occurring = P(A u B) = P(A) + P(B) - P(A n B) = 0.55 + 0.45 - 0.15 = 0.85

b) Probability of A and B occurring = P(A n B) = 0.15

c) Probability of just A occurring = P(A n B') = P(A) - P(A n B) = 0.55 - 0.15 = 0.40

d) Probability of just A or just B occurring = P(A n B') + P(A' n B) = 0.4 + (0.45 - 0.15) = 0.4 + 0.3 = 0.70