1. solve the following: a. let a and b be events in a sample space s such that p(a) = 0.41, p(b) = 0.46 and p(a / b) = 0.14. find p(a | b). a) 0.3415 b) 0.0217 c) 0.8913 d) 0.1609 e) 0.3043 f) none of the above. b. let a and b be events in a sample space s such that p(a) = 13? 50 , p(b) = 49? 100 , and p(a ? b) = 1? 10 . find p(b | ac ). hint: draw a venn diagram to find p(b ⊃ a). a) 0.7959 b) 0.1351 c) 0.5270 d) 0.6622 e) 1.8846 f) none of the above. c. suppose that a and b are independent events. if p(a) = 3/10 and p(b) = 1/2 , find p(a / b). a) 0.15 b) 0.03 c) 1.00 d) 0.08 e) 0.05 f) none of the above.