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Example 33 - Chapter 13 Class 12 Probability
Last updated at Feb. 15, 2020 by Teachoo
Transcript
Example 33 Coloured balls are distributed in four boxes as shown in the following table: A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the boxs III?Let A : Event that a black ball is selected E1 : Event that the ball is selected from box I E2 : Event that the ball is selected from box II E3 : Event that the ball is selected from box III E4 : Event that the ball is selected from box IV We need to find out the Probability of the ball drawn is from box III if it is black. i.e. P(E3|A) P(E3|A)= (๐(๐ธ3).๐(๐ด|๐ธ3))/(๐(๐ธ1)๐(๐ด|๐ธ1)+๐(๐ธ2)๐(๐ด|๐ธ2)+๐(๐ธ3)๐(๐ด|๐ธ3)+๐(๐ธ4)๐(๐ด|๐ธ4)) P(E1) = Probability that ball drawn is from box I = 1/4 P(A|E1) = Probability of that black ball is selected from Box I = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ )/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ ๐๐ ๐กโ๐ ๐๐๐ฅ) = 3/18 P(E2) = Probability that ball drawn is from box II = 1/4 P(A|E2) = Probability of that black ball is selected from Box II = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ )/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ ๐๐ ๐กโ๐ ๐๐๐ฅ) = 2/8 = 1/4 P(E3) = Probability that ball drawn is from box III = 1/4 P(A|E3) = Probability of that black ball is selected froAm Box II = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ )/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ ๐๐ ๐กโ๐ ๐๐๐ฅ) = 1/7 P(E4) = Probability that ball drawn is from box IV = 1/4 P(A|E4) = Probability of that black ball is selected from Box IV = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ )/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ ๐๐ ๐กโ๐ ๐๐๐ฅ) = 4/13 Putting values in Equation "P(E3|A)"=(๐(๐ธ3).๐(๐ด|๐ธ3))/(๐(๐ธ1)๐(๐ด|๐ธ1)+๐(๐ธ2)๐(๐ด|๐ธ2)+๐(๐ธ3)๐(๐ด|๐ธ3)+๐(๐ธ4)๐(๐ด|๐ธ4)) = (1/4 ร 1/7)/( 1/4 ร 3/18 + 1/4 ร 1/4 + 1/4 ร 1/7 + 1/4 ร 4/13 ) = (1/28)/( 1/24 + 1/16 + 1/28 + 1/13 ) = (1/28)/( (1/(4 ร 6) + 1/(4 ร 4) + 1/(4 ร 7)) + 1/13) = (1/28)/( ((4 ร 7 + 6 ร 7 + 6 ร 4)/(4 ร 6 ร 4 ร 7)) + 1/13) = (1/28)/((28 + 42 + 24)/(4 ร 6 ร 4 ร 7) + 1/13) = (1/28)/(94/(4 ร 6 ร 4 ร 7) + 1/13) = (1/28)/((94 ร 13 + 4 ร 6 ร 4 ร 7)/(13 ร 4 ร 6 ร 4 ร 7) ) = 1/((94 ร 13 + 4 ร 6 ร 4 ร 7)/(13 ร 4 ร 6) ) = (13 ร 4 ร 6)/( 94 ร 13 + 4 ร 6 ร 4 ร 7) = (13 ร 2 ร 6)/( 47 ร 13 + 2 ร 6 ร 4 ร 7) = 156/(611 + 336) = 156/947 = 0.164
Examples
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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 Not in Syllabus - CBSE Exams 2021
Example 28 Important Not in Syllabus - CBSE Exams 2021
Example 29 Important Not in Syllabus - CBSE Exams 2021
Example 30 Important Not in Syllabus - CBSE Exams 2021
Example 31 Important Not in Syllabus - CBSE Exams 2021
Example 32 Important Not in Syllabus - CBSE Exams 2021
Example 33 Important You are here
Example 34 Important Not in Syllabus - CBSE Exams 2021
Example 35 Important
Example 36 Important
Example 37 Important
Chapter 13 Class 12 Probability
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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.