"A airline charges $560 for a ticket to a popular destination. There are 80 seats on the plane, and the probability that any particular customer will miss their flight is 20%.
The airline overbooks the flight by 5 seats (selling a total of 85 tickets) If a customer shows up and there are no seats available, the airline must refund the full price of their ticket plus 40%
Find the expected amount the airline will pay."
I just want to make sure I'm thinking about this right.
I think E(x) could have the values 0, 1, 2, 3, 4, 5
If it's $0$, the airline pays nothing, exactly the right amount of people shows up. The chance of this happening is $binompdf(85, 0.80, 80)$
If it's $1$, the airline pays $540 + 540 * (0.4) = 756.$ The chance of this happening is $binompdf(85, 0.80, 81)$
If it's $2$, the airline pays $756 + 756 = 1512.$ The chance of this happening is $binompdf(85, 0.80, 82)$
And so on.
This all seems pretty straightforward, but when I go to calculate E(x), I come up with ~$0.052, a number that seems way too small.
Am I on the right track? Or did I make some sort of weird mistake.