What is the probability that SW Airlines flights will arrive late?

Math problem I am trying to solve:



Southwest Air has 80% of its flights arriving on time. A test is conducted by randomly selecting 17 flights and observing whether they arrive on time.



a) Find the probability that exactly 3 flights arrive late.



b) Find the probability that at least 3 flights arrive late.



Thanks for your help. An explanation would be helpful too.What is the probability that SW Airlines flights will arrive late?
P{on-time} = 0.8 so P{late} = 0.2



arriving late or not is a binomial outcome, so with n=17 and p=0.2

(a) P{3 late} = C(17, 3)*p^3*(1-p)^14 = 680*0.2^3*0.8^14 = 0.24

-- this is by the way, the most likely outcome



(b) at least 3 late means not-zero, not-one, and not-two late, so

P{at least 3 late} = 1 - P{0 late} - P{1 late} - P{2 late}

= 1 - 0.0225 - 0.0957 - 0.1914 = 0.69