A sample of 2000 randomly selected homeowners was selected from across the count

Question

A sample of 2000 randomly selected homeowners was selected from across the country in 2009. 400 of them had their house foreclosed upon. 100 declared bankruptcy. The probability that a homeowner is foreclosed upon, given that they have declared bankruptcy is 0.4.

a. What is the probability that a randomly selected homeowner declares bankruptcy and has their house foreclosed upon?

b. What is the probability that a randomly selected homeowner declared bankruptcy if their house was not foreclosed upon?

Explanation / Answer

probabilty of foreclosed =P(F)=400/2000=0.2

probabilty of bankruptcy =P(B)=100/2000=0.05

probability that a homeowner is foreclosed upon, given that they have declared bankruptcy=P(F|B)=0.4

a) probability that a randomly selected homeowner declares bankruptcy and has their house foreclosed upon

=P(F &B)=P(B)*P(F|B)=0.05*0.4=0.02

b)P(Fc &B)=P(B)-P(B &F) =0.05-0.02=0.03

also P(Fc)=1-P(F)=1-0.2=0.8

probability that a randomly selected homeowner declared bankruptcy if their house was not foreclosed upon

=P(B|Fc)=P(B &Fc)/P(Fc)=0.03/0.8=0.0375

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