A factory produces bulbs. The probability that one bulb is defective is 1 50 and they are packed in boxes of 10 . From a single box, find the probability that none of the bulbs is defective.

Let p be getting a defective bulb from a single box is a success. p = probability of getting a defective bulb = Favourable outcomes Total number of outcomes = 1 50 , q = 1 - p = 1 - 1 50 = 49 50 Let X denote the number of success in a sample of 10 trials. Then, X follows binomial distribution with parameters n = 10 and p = 1 50 and q = 1 - 1 50 = 49 50 We know that, P ( X = r ) = C r n p r q n - r . Therefore, required probability = P none of the bulb is defective = P X = 0 = C 0 10 1 50 0 49 50 ( 10 - 0 ) = C 0 10 49 10 50 10 = 49 50 10 .

A factory produces bulbs. The probability that one bulb is defective is 1 50 and they are packed in boxes of 10 . From a single box, find the probability that exactly two bulbs are defective

Let p be getting a defective bulb from a single box is a success. p = probability of getting a defective bulb = Favourable outcomes Total number of outcomes = 1 50 , q = 1 - p = 1 - 1 50 = 49 50 Let X denote the number of success in a sample of 10 trials. Then, X follows binomial distribution with parameters n = 10 and p = 1 50 and q = 1 - 1 50 = 49 50 We know that, P ( X = r ) = C r n p r q n - r . Therefore, required probability = P none of the bulb is defective = P X = 2 = C 2 10 1 50 2 49 50 ( 10 - 2 ) = C 2 10 49 8 50 10 = 45 × 49 8 50 10 .

A factory produces bulbs. The probability that one bulb is defective is 1 50 and they are packed in boxes of 10 . From a single box, find the probability that more than 8 bulbs work properly

Let p be getting a defective bulb from a single box is a success. p = probability of getting a defective bulb = Favourable outcomes Total number of outcomes = 1 50 , q = 1 - p = 1 - 1 50 = 49 50 Let X denote the number of success in a sample of 10 trials. Then, X follows binomial distribution with parameters n = 10 and p = 1 50 and q = 1 - 1 50 = 49 50 We know that, P ( X = r ) = C r n p r q n - r . Therefore, required probability is P ( X < 2 ) = P X = 0 + P X = 1 = C 0 10 49 10 50 10 + C 1 10 49 9 50 10 = 49 10 50 10 + 10 × 49 9 50 10 = 49 9 50 10 49 + 10 = 59 49 9 50 10 .