Question

Conditional Probability Problem

1) A foundry has 3 different production lines and wants to evaluate the performance of each line. The performance of each line is given below Percent of all parts that Percent of all parts that come from each line and Line X Line Y Line Z TOTAL come from each line 44% 36% 20% 100% are defective 3% 4% 1% 19% Parts from all 3 lines merge into a single conveyor to take them to inspection. Consider a part randomly picked from this conveyor. In your notation, use events X, Y, and Z, to represent that a part came from the respective line and D to represent that a part is defective. If you randomly select a part for inspection, what is the probability that.. a) ...the part came from Line Y? b) ...the part came from Line X and is defective? c) ...the part is defective given that the part came from Line Z? 2) A company has collected data on customer orders: If a customer receives a call from a salesperson, the probability the customer will place an order is 44% If a customer receives an email from a salesperson, the probability the customer will place an order is 18% in contacting customers, 23% receive a phone call and 77% receive an email. Every customer is contacted by one of the methods and no customers receive both a phone call and an email. . . . a) Define two relevant events for this situation-one related to method of contact and one b) Use your events from (a) to describe the probabilities 0.44, 0.18, and 0.23 that are given in c) For evaluation, a random customer is selected. What is the probability that this customer related to whether a customer places an order-and give each a letter. the description. received a phone call and placed an order?

Answer 1