## Elementary Statistics (12th Edition)

The bad case is if more than 19 passengers turn up. We need to find the probability of this and subtract it from 1 to get the probability of not being too many people. $P(X\leq19)=1-(P(X=20)+P(X=21))=1-{21 \choose 20} \cdot 0.9005^{20} \cdot 0.0995^1-{21 \choose 21} \cdot 0.9005^{21} \cdot 0.0995^0=1-0.2569-0.1107=0.6324.$ This is a quite low probability, the porbability of too many passengers is quite high, therefore it is not a good idea to book 21 passengers.