Example 37 - Chapter 13 Class 12 Probability
Last updated at Feb. 15, 2020 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) = (๐(๐ธ_1 ).๐(๐ด|๐ธ_1))/(๐(๐ธ_1 ).๐(๐ด|๐ธ_1)+๐(๐ธ_2 ).๐(๐ด|๐ธ_2) ) "P(E1)" = Probability that machine is correctly setup = 80% = 80/100 =0.8 P(A|E1) = Probability that machine produce 2 acceptable items if it have correct set up = ๐๐% ร ๐๐% = 90/100 ร 90/100 = 0.9 ร 0.9 = 0.81 "P(E2)" = Probability that machine is incorrectly setup = (100โ80)% = 20%=20/100 = 0.2 P(A|E1) = Probability that machine produce 2 acceptable items if it have incorrect set up = ๐๐% ร ๐๐% = 40/100ร40/100 = 0.4 ร 0.4 = 0.16 Putting values in the formula P(E1|A) = (๐(๐ธ_1 ).๐(๐ด|๐ธ_1))/(๐(๐ธ_1 ).๐(๐ด|๐ธ_1)+๐(๐ธ_2 ).๐(๐ด|๐ธ_2) ) = (0.8 ร ๐.๐๐)/(0.8 ร ๐.๐๐ + 0.2 ร ๐.๐๐) = 0.648/0.680 = 0.95
Examples
Example 1
Example 2
Example 3
Example 4
Example 5 Important
Example 6
Example 7 Important
Example 8
Example 9 Important
Example 10
Example 11 Important
Example 12 Important
Example 13 Important
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Example 18 Important
Example 19 Important
Example 20 Important
Example 21 Important
Example 22
Example 23
Example 24 Important
Example 25 Important
Example 26 Important
Example 27
Example 28 Important
Example 29 Important
Example 30 Important
Example 31 Important
Example 32 Important
Example 33 Important
Example 34 Important
Example 35 Important
Example 36 Important
Example 37 Important You are here
Chapter 13 Class 12 Probability
Serial order wise
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.