Of all mortgage foreclosures in the United States 47 are cau

Of all mortgage foreclosures in the United States, 47% are caused by disability. People who are injured or ill cannot work--they then lose their jobs and thus their incomes. With no income, they cannot make their mortgage payment and the bank forecloses. 11 mortgage foreclosures are audited by a large lending institution. (Give your answers correct to three decimal places.)

(a) Find the probability of P(Five or fewer of the foreclosures are due to disability)


(b) Find the probability of P(At least three foreclosures are due to a disability)

Solution

P(mortgage due to disability) =0.47

a) P(ans) = (0.47)^5 * (0.53)^6 +(0.47)^4 * (0.53)^7 +(0.47)^3 * (0.53)^8 +(0.47)^2 * (0.53)^9 +(0.47)^1 * (0.53)^10+ (0.53)^11

=0.0042057

b) P(ans) = 1-P(atmost 2)= 1- [(0.47)^2 * (0.53)^9 +(0.47)^1 * (0.53)^10+ (0.53)^11]

=1-0.002477792=0.9975