When someone buys a ticket for an airline flight there is a

When someone buys a ticket for an airline flight, there is a 0.0977 probability that the person will not show up for the flight. A certain jet can seat 9 passengers. Is it wise to book 11 passengers for a flight on the jet? Find the probability of there not being enough seats on the jet

Solution

The probability of showing up for the flight is 1-0.0977 = 0.9023.

It will overbook if at least 10 show up.

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    11      
p = the probability of a success =    0.9023      
x = our critical value of successes =    10      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   9   ) =    0.292842352
          
Thus, the probability of at least   10   successes is  
          
P(at least   10   ) =    0.707157648 [ANSWER]

This is a high probability, so it\'s not wise to book 11 passengers.