A manufacturer of halogen bulbs knows that 3 of the producti

A manufacturer of halogen bulbs knows that 3% of the production of their 100 W bulbs will be defective. a).What is probability that exactly 5 bulbs in a carton of 12 bulbs will be defective?

Solution

P = Probability of being defective = 0.03
1-P = Probability of not being defective = 0.97


12 C 5 = the number of combinations of 5 defects out of 12
(P)5(1-P)7= the probability for a single combination of 5 defects out of 12

The probability of exactly 5 defects = (12 C 5)(P)5(1-P)7