Question

There are three companies that make light bulbs: Company A, Company B, and Company C. From the annual output of bulbs, 70% are sold by A, 20% by B, and 10% by C. Some of these bulbs end up being defective. It is known from consumer reports that 5% of A’s bulbs are defective, while 10% of B’s bulbs and 15% of C’s bulbs are defective. You notice that a recently installed light bulb at school is defective. You know nothing else about the bulb. What is the probability that the school got the bulb from Company A? B? C?

Answer 1

We have d= Defective

P(A) = 0.70   P(d/A) = 0.05  

P(B) = 0.20 P(d/B) = 0.10

P(C) = 0.10 P(d/A) = 0.15

P(d) = P(A)*P(d/A) +P(B)*P(d/B) + P(C)*P(d/A)

P(d) =   0.70*0.05 + 0.20* 0.10 + 0.10 *0.15

P(d) = 0.035 + 0.020 +0.015

P(d) = 0.070

By Bay's theorem

P(A/d) =   

P(A/d) =

P(A/d) =      

P(A/d) = 0.5 Answer

similarly

P(B/d) = 0.020/0.070

P(B/d) = 0.2857 Answer

P(C/d)= 0.015/0.070

P(C/d) = 0.2143 Answer