Answer to Question #245560 in Statistics and Probability for Priya

Question

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

 

(a) Construct a tree diagram that illustrates all possible outcomes and probabilities

 

A chair is randomly selected.

 

(b) What is the probability that the chair that robot Q made is defective                                  

 

(c) What is the probability of findings a broken chair

 

(d) Given that a chair is defective, what is the probability that it was not made by robot R

 

Answer 1

(a)   Robot S makes 30% of the chairs

(b)   Required probability = 0.25 x 0.02 = 0.005

(c)  Probability of finding a broken chair = 0.25 x 0.02 + 0.45 x 0.03 + 0.30 x 0.05 = 0.0335

(d)   Required probability = (0.25 x 0.02 + 0.30 x 0.05)/0.0335 = 0.597