Three robots

In a workshop, three robots, Q, R, and S, are employed to make chairs    
Robot Q makes 25% of the chairs  
Robot R makes 45% of the chairs  
The remaining chairs are made by Robot S    

Evidence has shown that 2 percent of the chairs made by robot Q are defective, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective.    Construct a tree diagram that illustrates all possible outcomes and probabilities. A chair is randomly selected.    
What is the probability that the chair that robot Q made is defective? 
What is the probability of findings a broken chair?
Given that a chair is defective, what is the probability that it was not made by robot R?

Correct answer:

p1 =  0.02
p2 =  0.0335
p3 =  0.597

Step-by-step explanation:

Q=25%=10025=41=0.25 R=45%=10045=209=0.45 S=1QR=10.250.45=103=0.3  p2=Q 0.02+R 0.03+S 0.05=0.25 0.02+0.45 0.03+0.3 0.05=0.0335
PRD   p2 = P(R  D)  PRD=R 0.03/p2=0.45 0.03/0.0335=67270.403  p3=1PRD=10.403=0.597

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