Question

It is reported that 50% of all computer chips produced are defective. Inspec- tion ensures that only 5% of the chips legally marketed are defective. Unfortunately, some chips are stolen before inspection. If 1% of all chips on the market are stolen, find the probability that a given chip is stolen given that it is defective.

Answer 1

Answer:

probability of defective  = 0.0545

Probability of a chip to be stolen = 0.0917

Step-by-step explanation:

given data

all computer chips produced are defective = 50%

legally marketed are defective = 5 %

stolen = 1%

solution

we get here probability of defective that is

probability of defective = P ( insepected and defective + stolen and defective)  .........................1

put here value

probability of defective = (1 - 0.01) × 0.05 + 0.01*0.5

probability of defective  = 0.0545

and

So, Probability of a chip to be stolen given defective  =P (stolen and defective) ÷ P(defective)           ......................2

put here value

Probability of a chip to be stolen = 0.01 × 0.5 ÷ 0.0545

Probability of a chip to be stolen = 0.0917