Company credit card records. A bank officer is analyzing the transactions of a company credit card, controlled by three directors, director 1, 2 and 3. Of the transactions, 25% were made by director 1, 35% by director 2, and 40% by director 3. For i = 1, 2, 3, define Ei to be the event that the bank officer randomly selects a transaction by director i. The following probabilities describe the proportions of transactions in a foreign currency for directors 1, 2, and 3: P1foreign  E12 = 0.02, P1foreign  E22 = 0.05, and P1foreign  E32 = 0.01.

a. If a transaction in a foreign currency is analyzed by the bank officer, what is the probability that it was made by director 1?

b. If a transaction in a foreign currency is analyzed by the bank officer, what is the probability that it was made by director 2?

c. If a transaction in a foreign currency is analyzed by the bank officer, what is the probability that it was made by director 3?

d. Based on the probabilities, parts a–c, which director’s transaction in a foreign currency is most likely being analyzed by the bank officer? Applying the Concepts—Intermediate