Compute the number of cups of coffee that witi drinks

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Question: Ahren and Witi both love coffee. When Ahren is in the office, he drinks one cup of coffee with probability 0.6 and no cups of coffee with probability 0.4. When Witi is in the office, he drinks two cups of coffee with probability 0.5 and one cup with probability 0.5. Ahren and Witi always discard their empty coffee cups in the office wastebasket, and they are the only people to do so Xi asserts the following:

• The number of cups of coffee that Witi drinks at the office is irrelevant to Ahren's presence at the office.

• The number of cups of coffee that Ahren drinks at the office is irrelevant to Witi's presence at the office.

• The number of cups of coffee that Ahren drinks at the office is irrelevant to the number of cups of coffee that Witi drinks at the office.

Xi returns late from a client visit and finds that the office is empty. He doesn't know if Ahren, Witi, both, or neither had come to the office that day, but he recalls that the wastebasket was empty early in the morning, before any employees had arrived.

Given this information, how many of the following statements are true?

I. If Xi sees 1 cup in the wastebasket, then his probability that both Ahren and Witi were in the office that workday is greater than 0.1

II. If Xi sees 2 cups in the wastebasket, then his probability that only Witi came to the office that workday is 0.4

a. I only

b. II only

c. Both I and II

d. Neither T nor II

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