Answer Happy

(22pts) Three employees: Amy, Bob and Carl (A,B,C) work at a call center where they attempt to help customers. During a day they answered the following number of calls: Amy 100 calls • Bob 100 calls Carl 200 calls During these calls, sometimes Amy, Bob and Carl (A,B,C) were successfully (S) able to help the customer as follows: • Amy successfully helped customers for 95% of the calls that she received • Bob successfully helped customers for 90% of the calls that he received • Carl successfully helped customers for 10% of the calls that he received (a recent hire, still training) A customer, that placed a call to the call center, is randomly selected. For the answers that follow, please use the notation from the class and leave your answer in the form of an unevaluated expression to receive credit. Sample answer: P[DE] = 100/300 a) Determine the probability that Bob answered their call b) Given that Bob answered the call, determine the probability that they were successfully helped c) Determine the probability that Bob answered the call and that the customer was successfully helped d) Given that the customer was successfully helped, determine the probability that Bob answered the call