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# Determining Probability - Bank Loans and Card Decks

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A deck contains three drawers. Drawer 1 contains two gold coins. Drawer 2 contains one gold coin and on silver coin. Drawer 3 contains two silver coins. I randomly choose a drawer and then randomly choose a coin. If a silver coin is chosen, what is the probability that I chose drawer 3?

A customer has approached a bank for a loan. Without further investigation, the bank believes there is a 4% chance that the customer will default on the loan. The bank can run a credit check on the customer. The check will yield either a favorable or unfavorable report. From past experience, the customer believes that P(favorable report being received) | customer will default) = 1/40, and P(favorable report |customer will not default) = 99/100. If a favorable report is received, what is the probability that the customer will default on the loan?

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