Question

A company receives large shipments of parts from two sources. seventy percent of the shipments come from a supplier whose shipments typically contain 10fifectives, while the remainder are from a supplier 4.5 poisson distribution 171, whose shipments typically contain 20% defectives. a manager receives a shipment but does not know the source. a random sample of 20 items from this shipment is tested, and 1 of the parts is found to be defective. what is the probability that this shipment came from the more reliable supplier? (hint: use bayes‚äôtheorem.

Answer 1

To find the probability that the shipment came from the more reliable supplier, we can use Bayes' Theorem. Given the probabilities of shipments coming from each supplier, we can calculate the probability that the shipment came from the more reliable supplier given that 1 part is defective.

Step-by-step explanation:

To find the probability that the shipment came from the more reliable supplier, we can use Bayes' Theorem. Let A be the event that the shipment came from the more reliable supplier, and B be the event that 1 of the parts tested is defective. We want to find P(A|B), the probability that the shipment came from the more reliable supplier given that 1 part is defective.

Using Bayes' Theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

Given that 70% of the shipments come from the more reliable supplier and 30% from the less reliable supplier:

P(A) = 0.7, P(B|A) = probability of 1 defective part given that the shipment came from the more reliable supplier = binomial probability with n = 20, k = 1, and p = 0.1, P(B) = probability of 1 defective part regardless of the supplier = P(B|A) * P(A) + P(B|A') * P(A')

where A' is the complement of A.

Substituting the values into Bayes' Theorem:

P(A|B) = (binomial probability with n = 20, k = 1, and p = 0.1 * 0.7) / (P(B|A) * P(A) + P(B|A') * P(A'))