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Marginal & Conditional Probabilities

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A box contains six parts. Two of the parts are defective and four are ok. If three of the six parts are selected from the bin, how large is the sample space? Which counting rule did you use, and why? For this sample space, what is the probability that exactly one of the three sampled parts is defective?

A business has 20 employees. Six of these employees will be selected randomly to be interviewed as part of an employee satisfaction program. How many different groups of six can be selected?

Alex, Alicia, and Juan fill orders in a fast-food restaurant. Alex incorrectly fills 20% of the orders he takes. Alicia incorrectly fills 12% of the orders she takes. Juan incorrectly fills 5% of the orders he takes. Alex fills 30% of all orders, Alicia fills 45% of all orders, and Juan fills 25% of all orders. An order has just been filled.

a. What is the probability that Alicia filled the order?

b. If the order was filled by Juan, what is the probability that it was filled correctly?

c. Who filled the order is unknown, but the order was filled incorrectly. What are the
revised probabilities that Alex, Alicia, or Juan filled the order?

d. Who filled the order is unknown, but the order was filled correctly. What are the revised
probabilities that Alex, Alicia, or Juan filled the order?

Purchasing Survey asked purchasing professionals what sales traits impressed them most in a sales representative. Seventy-eight percent selected "thoroughness." Forty percent responded "knowledge of your own product." The purchasing professionals were allowed to list more than one trait. Suppose 27% of the purchasing professionals listed both "thoroughness" and "knowledge of your own product" as sales traits that impressed them most. A purchasing professional is randomly sampled.
a. What is the probability that the professional selected "thoroughness" or "knowledge of your own product"?
b. What is the probability that the professional selected neither "thoroughness" nor "knowledge of your own product"?
c. If it is known that the professional selected "thoroughness," what is the probability that the professional selected "knowledge of your own product"?
d. What is the probability that the professional did not select "thoroughness" and did select "knowledge of your own product"?