Question

y A and 25% from Factor The percentages of defectives produced by A and B are kn respectively. A customer has just bought a battery randomly from (a) What is the probability that the battery is defective? (b) If a battery is defective, what is the probability that it came from Facte 14-13. A retailer receives 75% of its batteries from Factory A and 25% to be 1% and 2%, wn to be 1%a0VB (Hint: Use Bayes' theorem in Problem 14-12.)

Answer 1

Here we have given

P(Factory A) = 0.75    P(A defective) =0.01
P(Factory B) = 0.25    P(B defective) = 0.02

(a)

P(Defective Battery) = P(Factory A)*P(A defective) + P(Factory B)*P(B defective)
= 0.75*0.01 + 0.25*0.02
= 0.0125

(b)

Let

P( A)=0.75

P( B) =0.25

P( D/A)=0.01

P( D/B)=0.02

Baye’s theorem used.

P( A/D) = P( D/A)* P( A) /( P( D/A)* P( A)+ P( D/B)* P( B))

=( 0.01*0.75)/(0.01*0.75+0.02*0.25)

    =0.60