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) =.22, P(A2) = .25, P(A3) = .28, P(A1?A2) = .11,P?(A1?A3)= .05, P(A2?A3) = .07, P(A1?A2?A3)= .01. Express in words each of the following events, and compute the probability of each event: a. A1?A2 b.A?1?A?2[?Hint:(? A1?A2) ?= ?(? A?1?A?2] c.A1?A2?A3 d. A?1?A?2?A?3 e. A?sub>1?A?2?A3 f.( A?1?A?;2) ?A3

Answer: Step 1: Given, a computer consulting firm presently has bids out on three projects. Let A = { awarded project i}, for i = 1,2,3. i Suppose that P(A )= 0.22 1 P(A )2 0.25 P(A )3 0.28 P(A1A ) 2 0.11 P(A 1A ) =30.05 P(A A ) = 0.07 2 3 P(A A A ) = 0.01 1 2 3 Here we need to compute the probability of each event: Step 2: a). To find P(1 A )2 P(A A ) = P(A ) + P(A )- P (A A ) 1 2 1 2 1 2 = 0.22 + 0.25 - 0.11 P(A 1A ) =20.36. Step 3: b). To find P( A 1 A2) A 1 A is2the event the firm is not awarded project 1 and not awarded project 2. P( A 1 A 2 = P(( A 1 A ))2= 1- P(A A )1 2 = 1 - 0.36 P(A 1 A2) = 0.64 Step 4: c). To find P(A A A ) 1 2 3 P(A A A ) = P(A )+ P(A )+ P(A )- P( A A )- P(A A ) -P(A A ) + (A A A 1 2 3 1 2 3 1 2 1 3 2 3 1 2 3 ) = 0.22 + 0.25 + 0.28 - 0.11 - 0.05 - 0.07 + 0.01 P(A 1A A2) = 3.53