web analytics

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

Slide26.JPG
Slide27.JPG

  1. Chapter 13 Class 12 Probability
  2. Serial order wise
Ask Download

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 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

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.
Jail