Your company operates a van service from the airport to down

Your company operates a van service from the airport to downtown hotels. Each van carries 7 passengers. Many passengers who reserve seats don’t show up – in fact., the probability is 0.2 that a randomly chosen passenger will fail to appear. Passengers are independent. If you allow 9 reservations for each van, what is the probability that more than 7 passengers will appear? Do a simulation to estimate this probability.

Solution

This is a binomial probability.

P(Appear) = 1 -0.2 = 0.8

P(X>7) = P(X=8) + P(X=9)

= 9C7 * (0.8)^7 * (0.2)^2 + 9C8 * (0.8)^8 * (0.2)^1

= 0.604 Answer