Question

Question:

Answer 1

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

• P(Defective)=0.05

• P(Sound)= 1- 0.05 = 0.95

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