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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?

https://brainmass.com/statistics/probability/probability-bank-failure-14968

#### Solution Preview

See the attached file for complete solution:
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 ...

#### Solution Summary

The expert calculates the probability of bank failure.

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