# Example 37

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 37 If a machine is correctly set up, it produces 90% acceptable items. If it is incorrectly set up, it produces only 40% acceptable items. Past experience shows that 80% of the set ups are correctly done. If after a certain set up, the machine produces 2 acceptable items, find the probability that the machine is correctly setup. Let E1 : Event that the machine is correctly setup E2 : Event that the machine is incorrectly setup A : Event that the Machine produce two acceptable items We need to find out the probability that the machine have a correct set up if it produce two acceptable item i.e. P(E1|A) P(E1|A) = 𝑃 𝐸1.𝑃(𝐴| 𝐸1)𝑃 𝐸1.𝑃(𝐴| 𝐸1)+𝑃 𝐸2.𝑃(𝐴| 𝐸2) Putting values in the formula P(E1|A) = 𝑃 𝐸1.𝑃(𝐴| 𝐸1)𝑃 𝐸1.𝑃(𝐴| 𝐸1)+𝑃 𝐸2.𝑃(𝐴| 𝐸2) = 0.8 × 𝟎.𝟖𝟏0.8 × 𝟎.𝟖𝟏 + 0.2 × 𝟎.𝟏𝟔 = 0.6480.680 = 0.95

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Example 37 You are here

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.