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Example 37 - If a machine is correctly set up, it produces 90% - Examples

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  1. Chapter 13 Class 12 Probability
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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 𝐸﷮1﷯﷯.𝑃(𝐴| 𝐸﷮1﷯)﷮𝑃 𝐸﷮1﷯﷯.𝑃(𝐴| 𝐸﷮1﷯)+𝑃 𝐸﷮2﷯﷯.𝑃(𝐴| 𝐸﷮2﷯) ﷯ Putting values in the formula P(E1|A) = 𝑃 𝐸﷮1﷯﷯.𝑃(𝐴| 𝐸﷮1﷯)﷮𝑃 𝐸﷮1﷯﷯.𝑃(𝐴| 𝐸﷮1﷯)+𝑃 𝐸﷮2﷯﷯.𝑃(𝐴| 𝐸﷮2﷯) ﷯ = 0.8 × 𝟎.𝟖𝟏﷮0.8 × 𝟎.𝟖𝟏 + 0.2 × 𝟎.𝟏𝟔﷯ = 0.648﷮0.680﷯ = 0.95

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