An industrial company is manufacturing locks using three production lines. Of th
ID: 3065064 • Letter: A
Question
An industrial company is manufacturing locks using three production lines. Of the total output, first production line is responsible for 20%, second production line for 45% and third production line for the rest. It is known from previous experience with the production lines that 7% of the output from first line is defective, 5% from second line and 3% from third line. A lock is chosen at random from the production line and found to be defective. (a) Find the probability that the lock came from first production line (b) Find the probability that the lock came from second production line (c) Find the probability that the lock came from third production line answer on paper preferred
Explanation / Answer
first production line, P(F) = 0.2
Second production line, P(S) = 0.45
Third production line, P(T) = 0.35
P(D|F) = 0.07, P(D|S) = 0.05 and P(D|T) = 0.03
Probability that a lock is defective,
P(D) = P(D|F)*P(F) + P(D|S)*P(S) + P(D|T)*P(T)
= 0.2*0.07 + 0.45*0.05 + 0.35*0.03
= 0.047
a)
P(F|D) = P(D|F)*P(F) / P(D)
= 0.2*0.07 / 0.047
= 0.2979 (required probability)
b)
P(S|D) = P(D|S)*P(S) / P(D)
= 0.45*0.05 / 0.047
= 0.4787 (required probability)
c)
P(T|D) = P(D|T)*P(T) / P(D)
= 0.35*0.03 / 0.047
= 0.2234 (required probability)