Determining Binomial Condition Probability of a Random Sample
I have a question about binomial probability involving a conditional event. This problem keeps tripping me up, because while I know how to calculate the binomial probability that a random variable is a failure, i don't know how to calculate the conditional probability of that variable.
My question is as follows:
70% of the total shipments come from factory A, of which 10% are defective.
30% of the total shipments come from factory B, of which 5% are defective.
A random shipment comes in, and a sample of 20 pints is taken, and 1 of the pints is defective.
What is the probability that this shipment came from the Factory A?