Let R be a random variable indicating revenue of airlines,and P(R) be the probability of that event.
Probability of turning up=0.01 and not turning up=1-0.01=0.99
Case 1:
0 people are not showing up or 51 people are showing up ,seat of 1 person will not be available as there are 50 seats and all 51 persons showed up,and they have to pay the compensation for a single person.Let this probability be P.
Case 2:
If at least 1 person not shows up or at most 50 person shows up,in all such cases,airlines will be earning 10k for all 51 tickets sold.Let this probability be Q=1-P (As, it's either the first case or second).
Distribution table goes as follows:-
$R_{i}$ |
$(51\times 10^{4})- 10^{5}$ |
$(51\times 10^{4})$ |
$P(R_{i})$ |
$(0.01)^{0}(0.99)^{51}$ |
$1-(0.01)^{0}(0.99)^{51}$ |
$E(R)=\sum_{i=1}^{2}R_{i}\times P(R_{i})$