Question

A salesman in a department store receives household appliances from three suppliers:
I, II, and III. From previous experience, the salesman knows that 2%, 1%, and 3% of the
appliances from suppliers I, II, and III, respectively, are defective. The salesman sells 35%
of the appliances from supplier I, 25% from supplier II, and 40% from supplier III. If an
appliance randomly selected is defective, find the probability that it comes from supplier
III.

Law of Total Probability must be used

Answer 1

P(Deffective | Supplier I) = 0.02

P( Deffective | Supplier II) = 0.01

P( Deffective | Supplier III) = 0.03

P( Supplier I) = 0.35

P( Supplier II) = 0.25

P( Supplier III) = 0.40

by using law of total probability,

P( Defective) = P(Deffective | Supplier I) *P( Supplier I) + P(Deffective | Supplier II) *P( Supplier II) +

P(Deffective | Supplier III) *P( Supplier III)

= (0.02 * 0.35) + ( 0.01 * 0.25) + (0.03 * 0.40)

= 0.0215

P( Supplier III | Defective) = P(Deffective | Supplier III) *P( Supplier III) / P( Deffective)
= (0.03*0.4) / 0.0215

=0.55814