Question

Two production lines produce the same part of computer. 50% of Line 1 produces 1,000 parts per week of which 100 are defective. 50% of Line 2 produces 2,000 parts per week of which 150 are defective.

a) If a quality control, choose a part randomly from the stock, determine the probability it is defective.

(b) If it is defective, calculate the probability it was produced by Line 1.

(c) Determine the probability if the quality control want to choose the perfect parts.

please help

Answer 1

P(   line 1   ) =    0.5
P(   line 2   ) =    0.5

          
P(   defective   | line 1)= 10/1000 = 0.1
P(   defective   | line 2)= 150/2000 = 0.075

a) P(defective) = P(line 1) * P(defective| line 1) + P(line 2) *P(defective| line 2) =                                    0.5*0.1+0.5*0.075=               0.0875

b) P(line 1| defective) = P(line 1)*P(defective| line 1)/P(defective)=               0.5*0.1/0.0875=       0.5714  

c)

P(non defective) = 1-0.0875 = 0.9125