A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = 0.22, P(A2) = 0.25, P(A3) = 0.28, P(A1 ∩ A2) = 0.13, P(A1 ∩ A3) = 0.03, P(A2 ∩ A3) = 0.07, P(A1 ∩ A2 ∩ A3) = 0.01.
Express in words each of the following events, and compute the probability of each event.
a) A1 ∪ A2
Express in words the event.
awarded only 1, awarded only 2, awarded neither 1 nor 2, awarded either 1 or 2, awarded either 1 or 2 (or both)
Compute the probability of this event.
b) A1' ∩ A2'
[Hint:
(A1 ∪ A2)' = A1' ∩ A2']
Express in words the event.
awarded only 1, awarded only 2, awarded neither 1 nor 2, awarded either 1 or 2, awarded either 1 or 2 (or both)
Compute the probability of this event.
(c) A1 ∪ A2 ∪ A3
Express in words the event.
awarded 1 but neither 2 or 3, awarded 3 but neither 1 nor 2, awarded at least one of these three projects, awarded all of the three projects, awarded none of the three projects
Compute the probability of this event.
(d) A1' ∩ A2' ∩ A3'
Express in words the event.
awarded 1 but neither 2 or 3awarded 3 but neither 1 nor 2 awarded at least one of these three projectsawarded all of the three projectsawarded none of the three projects
Compute the probability of this event.
(e) A1' ∩ A2' ∩ A3
Express in words the event.
awarded 1 but neither 2 or 3, awarded 3 but neither 1 nor 2, awarded at least one of these three projects, awarded all of the three projects, awarded none of the three projects
Compute the probability of this event.
(f) (A1' ∩ A2') ∪ A3
Express in words the event.
awarded only 1 or 2, awarded only 3, awarded neither of 1 and 2, or awarded 3, awarded either of 1 or 2, but not awarded 3, awarded at least one of these three projects
Compute the probability of this event.
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