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Question
A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that was produced by machine B?
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Solution
Let E1 = output of machine A; E2 = output of machine B
P(E1) = 60% = `60/100 = 3/5`
P(E2) = 40% = `40/100 = 2/5`
E = The item selected is bad.
P(poor output of machine A) = P(E|E1)
= 2%
= `2/100`
P(poor output of machine B) = P(E|E2)
= 1%
= `1/100`
Intended process
= `(1/100 xx 2/5)/((2/100 xx 3/5) + (1/100 xx 2/5))`
= `2/(6 + 2)`
= `1/4`
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