Finite Math: Probability

Question

A lot of 250 light bulbs contains 20 defective bulbs and 230 good bulbs. A sample of 4 different light bulbs is selected at random.

(a) What is the probability that all 4 bulbs selected are good?

(b) What is the probability that at least 3 of the bulbs selected are good?

Answer 1

Binomial: p = 230/250 = 23/25 = 0.92 so q = 1 - p = 0.08

a) (4 choose 4) (0.92)^4 (0.08)^0 = 0.71639296

b) Prob(3 or 4) = Prob(3) + Prob(4)

Prob(3) = (4 choose 3) * (0.92)^2 ( 0.08)^1 = 4 * 0.778688 * 0.08 = 0.24918016

0.24918016 + 0.71639296 = 0.96557312 = 96.557313%