NW 1.88 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 E; 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: P(foreign | E₁) = 0.02, P(foreign | E₂) = 0.05, and P(foreign| E3) = 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?

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NW
1.88 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 E, 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:
P(foreign| E₁) = 0.02, P(foreign | E₂) = 0.05, and
P(foreign| E3) = 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?
Transcribed Image Text:NW 1.88 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 E, 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: P(foreign| E₁) = 0.02, P(foreign | E₂) = 0.05, and P(foreign| E3) = 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?
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