Answer:
The probability that a ship that is declared defecive is sound is 0.375
Step-by-step explanation:
Let P(A|B) denote the conditional probability of A given B. We will make use of the equation
P(A|B) = P(A) × P(B|A) / P(B)
We have the probabilities:
- P(Declared Defective (detected) | Defective) = 0.95
- P(not Detected | Defective) = 1-0.95=0.05
- P(Declared Sound | Sound) = 0.97
- P(Declared Defective |Sound) = 1-0.97=0.03
We can calculate:
P(Declared Defective)= P(Detected | Defective)×P(Defective) + P(Declared Defective |Sound) ×P(Sound) = 0.95×0.05 + 0.03×0.95=0.076
P(S | Declared Defective) =
(P(Sound) × P(Declared Defective | Sound)) / P(Declared Defective)
=0.95×0.03 /0.076 =0.375
