If the probability of a no-show is 0.0988, then the probability that a ticketed passenger actually shows up is 1 - 0.0988 = 0.9012.
The probability that all 17 passengers show up - so flight is overbooked by 2 - is (0.9012)^17 = 0.1706. Surprisingly low, isn't it?
The probability that 16 passengers show up - so flight is overbooked by 1 - is 17 * (0.9012)^16 * (0.0988) = 0.3179. We multiply by 17 because there are seventeen passengers who may fail to show up.
So the probability of overbooking is 0.1706 + 03179 = 0.4885, or just under half - and over a third of those overbookings will require reassigning two passengers, not just one. I think any airline that overbooks basically half its flights is asking for trouble. The airline should definitely limit sales to sixteen seats - and then only if it is willing to deal with an angry ticketed passenger on 19% ((0.9012)^16 = 0.1893) of its flights.
The probability that all 17 passengers show up - so flight is overbooked by 2 - is (0.9012)^17 = 0.1706. Surprisingly low, isn't it?
The probability that 16 passengers show up - so flight is overbooked by 1 - is 17 * (0.9012)^16 * (0.0988) = 0.3179. We multiply by 17 because there are seventeen passengers who may fail to show up.
So the probability of overbooking is 0.1706 + 03179 = 0.4885, or just under half - and over a third of those overbookings will require reassigning two passengers, not just one. I think any airline that overbooks basically half its flights is asking for trouble. The airline should definitely limit sales to sixteen seats - and then only if it is willing to deal with an angry ticketed passenger on 19% ((0.9012)^16 = 0.1893) of its flights.
