# Example 33 - Chapter 13 Class 12 Probability

Last updated at Feb. 15, 2020 by Teachoo

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

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Example 12 Important

Example 13 Important

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Example 25 Important

Example 26 Important

Example 27 Deleted for CBSE Board 2021 Exams only

Example 28 Important Deleted for CBSE Board 2021 Exams only

Example 29 Important Deleted for CBSE Board 2021 Exams only

Example 30 Important Deleted for CBSE Board 2021 Exams only

Example 31 Important Deleted for CBSE Board 2021 Exams only

Example 32 Important Deleted for CBSE Board 2021 Exams only

Example 33 Important You are here

Example 34 Important Deleted for CBSE Board 2021 Exams only

Example 35 Important

Example 36 Important

Example 37 Important

Chapter 13 Class 12 Probability

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.