a factory produces electric bulbs by three plants: plants-1 ,plants-2, plants-3, produces 3000, 4000 and 3000 units respectively.past experiences shows that 2% products of plant-1 ,3% products of plant -2, 1% products of plant -3 are defectives. a bulb is selected randomly and found defective. find the probability that it is produced by plant -1
Let "A" denote the event "electric bulb is produced by plant -1".
Let "B" denote the event "electric bulb is produced by plant -2".
Let "C" denote the event "electric bulb is produced by plant -3".
Let "D" denote the event "electric bulb is defective".
Given
"P(A)=0.3, P(B)=0.4, P(C)=0.3,""P(D|A)=0.02, P(D|B)=0.03, P(D|C)=0.01"
By Bayes' Rule
"=\\dfrac{P(A)P(D|A)}{P(A)P(D|A)+P(B)P(D|B)+P(C)P(D|C)}"
"=\\dfrac{0.3(0.02)}{0.3(0.02)+0.4(0.03)+0.3(0.01)}=\\dfrac{2}{7}"
The probability that electric bulb is produced by plant -1 given that it is defective is "\\dfrac{2}{7} ."
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