NDA2023MathematicsProbabilityActual
Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. 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?
Options
- A0.10
- B0.19
- C0.45
- D0.95
Correct answer
B. 0.19
Step-by-step solution
Let E ₁= design is faulty E ₂= design is not faulty A ^2= building is collapses Since, P (E₁ )=10 %= 1 10 aligned & P ( E ₂ )=90 %= 9 10 & P ( ~A / E ₁ )=95 %= 19 20 & P ( ~A / E ₂ )=45 %= 9 20 aligned Now P ( E A )= P (E₁ ) P (A / E₁ ) P (E₁ ) P (A / E₁ )+P (E₂ ) P (A / E₂ ) = 1 10 19 20 1 10 19 20 + 9 10 9 20 = 19 100 =0.19