Question

All old skyscrapers in the city of Karachi are being rehabilitated. 25% of all old skyscrapers in the city will need geotechnical underpinning. If an old skyscraper needs underpinning, the probability that it will need an expert to supervise the overall rehabilitation work is 0.85. If it does not need underpinning, the probability that it will need a supervising expert is 0.14.

1. Draw a probability tree for this problem. Show all probability values at each branch.
2. For any randomly selected skyscraper, what is the probability that it does not need an expert?
3. What is the probability that a randomly selected old skyscraper does not need an expert given that it needs underpinning?
4. What is the probability that a randomly selected old skyscraper does not need an expert, and needs underpinning?

v.What is the probability that a randomly selected old skyscraper needs underpinning given that it does not need an expert?

Answer 1

let probability of needing underpinning and expert are P(A) and P(B) respectively.

i)

P(AnB)-0.2125 P(BIA):0.85 P(BcIA)-0.15 P(AnBc-0.0375 P(AcnB)-0.105 P(Ac)-0.7 P(BIAc) 0.14 P(Bc Ac-0.86 P(AcnBc 0.645

ii)

P(Bc) =P(A n Bc)+P(Ac n Bc) =P(A)*P(Bc|A)+P(Ac)*P(Bc|Ac)=0.25*(1-0.85)+0.75*(1-0.14)

=0.0375+0.645 =0.6825

iii)

P(Bc|A )=1-P(B|A) =1-0.85 =0.15

iv) P(A n Bc) =P(A)*P(Bc|A) =0.25*(1-0.85)=0.0375

v) P(A|Bc) =P(A n Bc)/P(Bc) =0.0375/0.6825=0.0549