Probability decision analysis

Question

Bank Chicago is investigating mistakes at three of its branches to try to determine the major causes of these mistakes. Branch three has the lowest percentage of mistakes, with one percent of transactions having mistakes of some kind. Branch two has the next highest with two and a half percent errors, and branch one has four percent, assumed to be because it has the employees with the least amount of experience. 

The number of transactions/day from each bank are as follows:

Bank 1 - 1000

Bank 2 - 2000

Bank 3 - 2000

If a mistake is being investigated, what is the probability it came from Bank 2?

Round your answer to the nearest three (3) decimal places.

Answer 1

expected number of mistakes

bank 1 = 1000 * 0.04 = 40

bank 2 = 2000 * 0.025 = 50

bank 3 = 3000 * 0.01 = 30

probability bank 2 = 50/120 = 5/12