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10 March, 15:30

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?

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  1. 10 March, 17:11
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    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%)
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