Answer to Question #242422 in Statistics and Probability for GAD

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

Let us denote the events as follows:

F= The design is faulty

C=The building collapses

Then, we are given the probabilities:

$P(F)=10\; \%=0.1 \\ P(\bar{F})=1-0.1=0.9 \\ P(C|F)=95\; \%=0.95 \\ P(C| \bar{F})=45\; \%=0.45$

The required probability is P(F|C), which, using Bayes’ theoreme, can be obtained as:

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