Question

a manufacturer buys 38% of its chips from a factory in st. louis, and the remainder from a factory in los angeles. of the chips from st. louis, 3.5% are defective. of the chips from los angeles, 1.1% are defective. (a) find the probability that a chip is defective and made in st. louis. (b) find the probability that a chip is defective and made in los angeles. (c) find the probability that a chip is defective.

Answer 1

The probability that a chip is defective and made in St. Louis is 0.0133, the probability that a chip is defective and made in Los Angeles is 0.00682, and the overall probability that a chip is defective is 0.02012.

Step-by-step explanation:

To find the probability that a chip is defective and made in St. Louis, we multiply the probability of a chip being from St. Louis (38%) by the probability of a chip from St. Louis being defective (3.5%):

P(Defective and St. Louis) = 0.38 x 0.035 = 0.0133

To find the probability that a chip is defective and made in Los Angeles, we multiply the probability of a chip being from Los Angeles (62%) by the probability of a chip from Los Angeles being defective (1.1%):

P(Defective and Los Angeles) = 0.62 x 0.011 = 0.00682

To find the probability that a chip is defective, we add the probabilities of a chip being defective and made in St. Louis and a chip being defective and made in Los Angeles:

P(Defective) = P(Defective and St. Louis) + P(Defective and Los Angeles) = 0.0133 + 0.00682 = 0.02012