Question

Electric motors coming off four assembly lines are pooled for storage in a common stockroom, and the room contains an equal number of motors from each line. Motors are periodically sampled from that room and tested. It is known that 10% of the motors from line I are defective, 5% of the motors from line II are defective, 3% from line III are defective and 1% from line IV are defective. If a motor is randomly selected from the stockroom and found to be defective, find the probability that it came a) from line I b) from line II c) from line III d) from line IV.

Answer 1

P(defective) =P(line 1)*P(defective|line 1)+P(line II)*P(defective|line II)+P(line III)*P(defective|line III)+P(line IV)*P(defective|line IV)

=0.25*0.1+0.25*0.05+0.25*0.03+0.25*0.01 =0.0475

a)

P(Line 1|defective) =P(line 1)*P(defective|line 1)/P(defective) =0.25*0.1/0.0475 =0.5263

b)

P(Line II|defective) =0.25*0.0.5/0.0475 =0.2632

c)

P(Line III |defective) =0.25*0.03/0.0475 =0.1579

d)

P(Line IV|defective) =0.25*0.01/0.0475 =0.0526