Answer
0.3676, not a good idea to book 21 passengers.
Work Step by Step
The bad case is if more than 19 passengers turn up. We need to find the probability of this. $P(X>19)=P(X=20)+P(X=21)={21 \choose 20} \cdot 0.9005^{20} \cdot 0.0995^1+{21 \choose 21} \cdot 0.9005^{21} \cdot 0.0995^0=0.2569+0.1107=0.3676. $ This is a quite high probability, therefore it is not a good idea to book 21 passengers.
