Question: Joan is trying to decide which of two sales opportunities to take.
- In the first, she makes three independent calls. Payoffs are $570, $525, and $465, with respective probabilities of 0.57, 0.41, and 0.35.
- In the second, she makes eight independent calls, with probability of success on each call p = 0:57. She realizes $150 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.
a. Which alternative offers the maximum possible gain?
b. Compare probabilities in the two schemes that total sales are at least $600, $900, $1000, $1100.
c. What is the probability the second exceeds the first_ i.e., what is P (Y > X)?