Question

The Riverton Branch of the National Bank of Wyoming has 10 real estate loans over $1,000,000. Of these 10 loans, 3 are “underwater.” A loan is underwater if the amount of the loan is greater than the value of the property. The chief loan officer decided to randomly select two of these loans to determine if they met all banking standards. What is the probability that neither of the selected loans is underwater?

Answer 1

The number of ways of randomly 2 loan $n\left(S\right)=10C_2=\frac{10\times 9}{2\times 1}=\frac{90}{2}=45$

The number of ways of selecting non - underwater loan $n\left(E\right)=\left(10-3\right)C_2=7C_2=\frac{7\times 6}{2\times 1}=21$

$p\left(E\right)=Probability=\frac{n\left(E\right)}{n\left(S\right)}=\frac{21}{45}=\frac{7}{15}$

The probability that neither of the selected loans is underwater is $\frac{7}{15}$ .