Did not need repair find the probablility that it was produced by company C?

Question

Companies A, B and C produce 20%, 50%, and 30%, repectively, of major appliances sold under the Kenmore name in Lea County. In Lea County 3% of company A appliances need repair within 1 year of service, 2% of company B appliances need repair within 1 year of service, and 1% of company C appliances need repair within 1 year of service.
If you bought a Kenmore appliance and it did not need repair within the first year, find the probability that it was produced by compancy C?

Answer 1

You need to use Bayes' Theorem:
NR = No Repair and R = Repair
A, B or C = Company A B or C

P(C | NR ) = P(NR | C)*P(C)/[P(NR | A)*P(A) + P(NR | B)*P(B) + P(NR | C)*P(C) ]

P(NR | C) = 1-1% = 0.99 P(C) = 30%
P(NR | B) = 1- 2% = 0.98 P(B) = 50%
P(NR | A) = 1-3% = 0.97 P(A) = 20%

P(C | NR) = (30% * 0.99)/[(0.99*30%) + (0.98*50%) + (0.97*20%)]

= 0.297 / [ 0.2997 + 0.49 + 0.194] = 0.297 / 0.981 = .30275

So there is a 30.275% chance the item was produced by company C given there were no repairs the first year.