Question:

Suppose that chips for an intergrated circuit are tested and

thatthe probability that they

are detected if they are defective is 0.95 and the

probabilitythat they are declared

sound if in fact they are sound is 0.97. If 0.05% of the chops

aredefective, what is the

probability that a ship that is declared defecive is sound?

Question

Jarrett

Mathematics

14 January, 06:04

Question:

Suppose that chips for an intergrated circuit are tested and

thatthe probability that they

are detected if they are defective is 0.95 and the

probabilitythat they are declared

sound if in fact they are sound is 0.97. If 0.05% of the chops

aredefective, what is the

probability that a ship that is declared defecive is sound?

+2

Answers (1)

Know the Answer?

Ryan Barron · Answer 1

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