In Exercise 13, Ai={ awarded project i} , for I =1,2,3. Use the probabilities given there to compute the following probabilities, and explain in words the meaning of each one. a. P(A2|A1) b.P(A2 ?A3|A1) c.P(A2 ?A3|A1) d.P(A1 ?A2 ?A3|A1 ?A2 ?A3)

Answer: Step 1 of 4 Here, A = {awarded project i}, for i = 1, 2, 3 and suppose that P(A ) = 0.22, P(A ) = 0.25, i 1 2 P(A ) = 0.28, P(A A ) = 0.11, P(A A ) = 0.05, P(A A )= 0.07, P(A A A ) = 0.01 3 1 2 1 3 2 3 1 2 3 P(A 1A ) 2 A. P(A |2 ) 1 P( A ) 1 0.11 = 0.22 = 0.5 Step 2 of 4 P((A A ) A ) B. P(A A |A ) = 2 3 1 2 3 1 P( A ) 1 P(A 1 A 2 ) 3 = P(A )1 = 0.01 0.22 = 0.0454