A hospital receives two-fifths of its flu vaccine from Company A and the remaine

Question

A hospital receives two-fifths of its flu vaccine from Company A and the remainer from Company B. Each shipment contains a large number of vials of vaccine. From Company A, 3% of the vials are ineffective; from Company B, 2% are ineffective. A hospital tests n=25 randomly selected vials from one shipment and finds that 2 are ineffective. What is the conditional probability that this shipment came from Company A?

Answer is .54229, but I'm more concerned with the detailed steps on HOW to solve the problem. Thanks for the guidance.

Explanation / Answer

out of 25:

10 are from A
15 are from B

P = (.03x10)/(.03x10 + .02x15) = .5

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