Anthony Papantonis, owner of Nauset Construction, is bidding on two projects, A and B. The probability that he wins project A is 0.50 and the probability that he wins project B is 0.80. Winning Project A and winning Project B are independent events.

a. What is the probability that he wins project A or project B?

b. What is the probability that he does not win either project?

a) the probability of winning A and B is 0.4 (40%)

b) the probability of not winning either project is 0.1 (10%)

Step-by-step explanation:

if 2 events are independent then

P (A∩B) = P (A) * P (B)

where

P (A) = probability of winning project A

P (B) = probability of winning project B

P (A∩B) = probability of winning projects A and B

replacing values

P (A∩B) = P (A) * P (B) = 0.50 * 0.8 = 0.4

b) since

P (A∪B) = P (A) + P (B) - P (A∩B) = 0.50 + 0.8 - 0.4 = 0.9

where

P (A∪B) = probability of winning A or B

therefore

probability of not winning either project = 1 - P (A∪B) = 1 - 0.9 = 0.1 (10%)