Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or <strong>NOT</strong>. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?
- A. 0.10
- B. 0.19 ✓
- C. 0.45
- D. 0.95
Correct Answer: B. 0.19
Explanation
Let F be the event of faulty design, C be the event of collapse. P(F) = 0.10, P(F') = 0.90. P(C|F) = 0.95, P(C|F') = 0.45. By Bayes' Theorem, P(F|C) = \frac{P(C|F)P(F)}{P(C|F)P(F) + P(C|F')P(F')} = \frac{0.95 \times 0.10}{0.95 \times 0.10 + 0.45 \times 0.90} = \frac{0.095}{0.095 + 0.405} = \frac{0.095}{0.500} = 0.19.
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