Pax turn up only 95% of the time. Airline can fit 40 pax but sells 42 tickets. What is the probability that 42 show up?

Answer 1

1 specific person shows up with probability = 95%

2 specific people show up with probability= .95^2 = 90.25%

....

n specific ticket holders show up with probability = .95^n

42 show up with probability .95^42 = about .116 = 11.6%