Problem : A bike manufacturer has a plant in Minneapolis and another in Philly. The Minneapolis plant produces 70% of the bikes, of which 1% are defective. The Philly plant produces the other 30%, of which 0.5% are defective.

1: What percentage of bikes made by this company are defective? a) 1% b) 0.85% c) 0.5% d) 1.5%

I figured that 1% of 70% of production is 0.7% of total production. 0.5% of 30 is 30/100 = 0.3/2 = 0.15. 0.15+0.7= 0.85 so B

2. A bike made by this company is found to be defective. What is the probability that it was produced by the Minneapolis plant? a) .824 b) .176 c) .699 d) .301

3. non defective. What is the probability that is it made by the Minneapolis plant? a) .824 b) .176 c) .699 d) .301

4. A bike made by this company is found to be defective. Probability it was produced by the philly plant? a) .824 b) .176 c) .699 d) .301

5. Non defective. Probability made by Philly plant? a) .824 b) .176 c) .699 d) .301

1 is answered correctly to my knowledge.

Work for the rest is: D = defective, ND = non-defective, M= Minneapolis, P = philly

P(M) 0.7 P D/M = 1/70 P(M AND D) (0.7)(1/70) = 0.01 P M/D = .01/1

P(M) 0.7 P ND/M = 69/70 P (M AND ND) (0.7)(69/70) = 0.69 P M/ND = 0.69/1

P(P) 0.3 P D/P = 0.5/30 P(P AND D) (0.3)(0.5/30) = 0.005 P P/D = .005/1

P(P) 0.3 P ND/P = 29.5/30 P(P AND ND) (0.3)(29.5/30) = 0.295 P P/ND = 0.295/1

p(C)= 1.0

I have done something wrong here. Can someone please tell me what I am missing? I'm not asking for an answer. I am asking for how I should set this up.