Maeve and Bill are considering the purchase of a home in New

Maeve and Bill are considering the purchase of a home in Newton. The probability that a house will have a roof leak is 0.20. The probability that a house will have a problem with the heating system is 0.30. The probability of both a roof leak and a heating problem is 0.06. What is the probability that the home they purchase will have a roof leak or a problem with the heating system? What is the probability of having just a heating problem? Given that the home had a problem with the heating system, what is the probability it has a roof leak? Given we know that a house has at least one of the two problems(roof leak, heating ), what is the probability it will have both problems?

Solution

P(roof leak=A)=0.20

P(problem with heating system=B)=0.30

P(both)=0.06

a) P(A or B) = P(A) +P(B) -P(both) = 0.5-0.06 = 0.44

b) P(B) -P(both) = 0.30-0.06 = 0.24

c) P(A/B) = P(both) /P(B) = 0.06/0.3=0.2

d) let P(atleast one of two problems) =P(C)= 0.2*07 + 0.8*0.3 + 0.06 = 0.44

     Let P(both problems) =P(D) = 0.06

P(D/C) = P(D and C)/ P(C)= 0.06/0.44=6/44=3/22 =0.1363636= 0.1364