Question

Suppose there is a chance for a newly constructed building to collapse whether the design is faulty or not. The chance that the design faulty is 10%.the chance that the building collapse is 95% if the design is faulty and otherwise it is 45%.It is seen that the building collapsed. What is the probability that it is due to faulty design issued by suburbs?

Answer 1

$P(F/C)= \frac{P(F)P(C/F)}{P(F)P(C/F)+P(\bar{F})P(C/\bar{F})}\\ =\frac{0.1*0.95}{0.1*0.95+0.9*0.45}\\ =0.19$