MHB Statistics Question Probability

[kwiddoes23]

Hello, I was hoping someone could help explain how to do this problem. I have been stuck on it for a while now. Thanks! Any advice is appreciated. Also, for people just out to block questions, I AM NOT ASKING FOR THE ANSWER - I AM NOT TRYING TO CHEAT. I just would like help.

A hospital receives 1/5 of its flu vaccine shipments from Company X and the remainder of shipments from Company Y. Each shipment contains a very large number of vaccine vials. In Company X’s shipments, it is known that 10% of the vials are ineffective. For Company Y, 2% of the vials are ineffective. The hospital just received a new shipment, but is not certain if it came from Company X or Y. The hospital tested 30 randomly selected vials from the new shipment and found only one vial is ineffective.

(a) Suppose that if the shipment came from Company X. Then what is the probability
of finding only 1 ineffective vial out of 30?

(b) Suppose that if the shipment came from Company Y. Then what is the probability
of finding only 1 ineffective vial out of 30?

(c) Use Bayes’ theorem (Law of total probability) to calculate probability that this
shipment came from Company X given the test result.

(d) Use Bayes’ theorem to calculate probability that this shipment came from Company
Y given the test result.

 

[Greg]

Hello kwiddoes23 and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?