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A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project...

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) = 0.14, P(A1 ∩ A3) = 0.04, P(A2 ∩ A3) = 0.06, 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 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.

(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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