Question: James is trying to decide which of two sales opportunities to take.
- In the first, he makes three independent calls. Payoffs are $310, $380, and $350, with respective probabilities of 0.35, 0.41, and 0.57.
- In the second, he makes eight independent calls, with probability of success on each call p = 0:57. He realizes $100 profit on each successful sale.
- Let X be the net profit on the first alternative and Y be the net gain on the second. Assume the pair {X; Y} is independent.
- Which alternative offers the maximum possible gain?
- What is the probability the second exceeds the first_ i.e., what is P (Y > X)?
- Compare probabilities in the two schemes that total sales are at least $600, $700, $750.