In a bolt factory, machines A , B and C manufacture respectively 25%, 35% and 40% of the total bolts. Of their output 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. Then the probability that the bolt drawn is defective is
Text Solution
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Let 
and A be the events defined as follows:
the bolts is manufactured by machine A ; 
the
bolts is manufactured by machine B ; 
the bolts is
manufactured by machine C , and A = the bolt is defective.
Then .
Probability that the bolt drawn is defective given the condition that it is manufactured by machine A = 5/100.
Similarly 
and 
.
Using the law of total probability, we have
.
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