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Probability of bank failure

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In a state that is going through financial difficulties, it is beleived that 5% of banks will fail. It is known that deposits of 90% of the banks in the state are insured by the FDIC. It is also believed that 3% of the banks insured by the FDIC will fail.

a) What is the probability that, for a randomly chosen bank, the bank has deposits protected by the FDIC and the bank will fail?

b) What is the probability that for a randomly chosen bank, the bank has deposits covered by the FDIC or the bank will fail?

c) What percentage of banks that go under have deposits protected by the FDIC?

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The expert calculates the probability of bank failure.

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a) What is the probability that, for a randomly chosen bank, the bank has deposits protected by the FDIC and the bank will fail?

Probability that the bank is protected by FDIC=90/100
Probability that given the bank is protected by FDIC it will ...

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