11.7% of the population is 65 or older. Find the probability that the following number of persons selected at random from 20 people are 65 or older.

1) Probability that all are 65 or older?
2) Probability that at most 2 are 65 or older?

This is a binomial distribution with n = 20 and p = 0.117

B\ \sim \ (20,0.117)

For all being older...

P(\text{All are 65 or older}) = \(20\\ 20\) (0.117)^{20}

For 2 being older...

P(\text{2 are 65 or older}) = \(20\\ \ 2\) (0.117)^{2}(1-0.117)^{18}

Can you work these out?