Its asserted that 90 percent of the cars approaching an individual toll both in New Jersey are equipped with an E-Z pass transponder. Find the probability in a sample of 6 cars.

Question

A: At least three will have a transponder?

Answer 1

this is binary ... transponder (t) or no transponder (n)
... p(t) = .9 ... p(n) = .1

(t + n)^6 = t^6 + 6 t^5 n + 15 t^4 n^2 + 20 t^3 n^3 + ... + n^6

sum the 1st four terms
... p(t) = .9^6 + (6 * .9^5 * .1) + (15 * .9^4 * .1^2) + (20 * .9^3 * .1^3)