A bolt is manufactured by 3 machines A,B,C. A turns at twice as many items as B and
machines B and C produce equal number of items.2 % of bolts produced by A and B are
defective and 4% of bolts produced by C are defective. All bolts are put into 1 stock pile and 1 is
chosen from the pile. What is the probability that it is defective
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Step-by-step explanation:
Let A =the event in which item has been produced by machine A. and so on.
D =The event of the item being defective.
P(A)= 1/2 ,P(B)=1/4
P(D/A)=P(An item is defective, given that A has produced it)
=2/100 =P(D/B)
P(D/C) =4/100
By theorem of total productivity,
P(D)= P(A)* P(D/A)+P(B)*(D/B)+P(C)*(D/C)
=1/2 x 2/100 + 1/4 x 2/100 + 1/4 x 4/100
=1/40
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