What is the probability that these cars will fail the emissions test?!

Question

Of all the registered automobiles in a city, 9% fail the emissions test. Eight automobiles are selected at random to undergo an emissions test. Round the answers to four decimal places.

Questions below (4) thank you

Find the probability that exactly four of them fail the test

Find the probability that fewer than four of them fail the test.

Find the probability that more than three of them fail the test.

Would it be unusual for more than one of them to fail the test.

Answer 1

Use the binomial theorem

Let k = the number of cars that fail.

let P(fail) =p

let P(pass) = q

Then P(k) = (8ck)(p^k)(q^q)

Just plug in k, p and q. Note that only k changes,