Answer to Question #264167 in Statistics and Probability for Faru

Question #264167

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


1
Expert's answer
2021-11-11T13:03:16-0500

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".


"3000+4000+3000=10000"

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


"P(A|D)"

"=\\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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