A bank determines that 10% of all borrowers default loans. Answer the following questions, when, in a given month, 15 loans are defaulted. Let X be the number of defaulted loans. a. What is the probability that no loans are defaulted? Show your calculations. b. What is the probability that less than two loans are defaulted? Show your calculations. c. What is the probability that more than three loans are defaulted? Show your calculations.

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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A bank determines that 10% of all borrowers default loans. Answer the following questions, when, in a given month, 15 loans are defaulted. Let X be the number of defaulted loans.
a. What is the probability that no loans are defaulted? Show your calculations.
b. What is the probability that less than two loans are defaulted? Show your calculations.
c. What is the probability that more than three loans are defaulted? Show your calculations.

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Givenp=0.10sample size(n)=15Let "x" be the no.of loans are defaultedx~Binomial(n=15,p=0.10)P(X=x)=(nx)×px×(1-p)n-x                      , x=0,1,...,n

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