Expected revenue in case of flight overbooking An airline operates a flight having 50 seats. As they expect some passenger to not show up, they overbook the flight by selling 51 tickets. The probability that an individual passenger will not show up is 0.01, independent of all other tourists. Each ticket costs 10,000 and is non refundable if a tourist fails to show up. If a tourist show up and a set is not available, the airline has to pay a compensation of 100,000 to that passenger. What is the expected revenue of the airline?
My solution
Let $X$ be a random variable that represents the number of passengers that shows up to the flight and $r(X)$ the revenue of the company when a given number of passengers shows up. Then,
$$ X \sim Bin(51,0.99) $$
If the company didn't have to pay a compensation to the passenger in the case that he shows up and a seat is not available, then the company's expected revenue would be
$$E_X(r(X)) = 10,000 np = 504,900$$
But in the case that a passenger shows up and no seat is available, the company must pay 100,000 to that passenger. Note that this situation occurs only when all the 51 passengers shows, which occurs with probability $0.99^{51}=0.598956006$. Hence, the expected loss in this situation to the company would be
$$0.99^{51} (-100,000)=-59,895.6006$$
And the company's expected revenue accounting for overbooking is
$$504,900 - 59,895.6006 = 445,004.399$$
Book's answer: $450,104.4$
I don't understand where my logic is flawed. Can you help me with it?

Thanks to @Xi'an I was able to see what I was doing wrong.
The point is that all the 51 seats were sold, independent of the number of passengers showing to the flight. Hence the expected company's revenue is
51 × 10,000 - (0.99)^{51} × 100,000 = 450,104.4
