Question

Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans. a. What is the probability that 3 loans will be defaulted? b. What is the probability that at least 3 loans will be defaulted?

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DEFINITIONS

Formula Poisson probability\textbf{Poisson probability}:

P(X=k)=μkeμk!P(X=k)=\dfrac{\mu^k e^{-\mu}}{k!}

Complement rule\textbf{Complement rule}:

P(A)=P(not A)=1P(A)P(\sim A)=P(\text{not }A)=1-P(A)

Addition rule\textbf{Addition rule} for disjoint or mutually exclusive events:

P(AB)=P(A or B)=P(A)+P(B)P(A\cup B)=P(A\text{ or }B)=P(A)+P(B)

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