



Examples
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 Deleted for CBSE Board 2022 Exams
Example 28 Important Deleted for CBSE Board 2022 Exams
Example 29 Important Deleted for CBSE Board 2022 Exams
Example 30 Important Deleted for CBSE Board 2022 Exams
Example 31 Important Deleted for CBSE Board 2022 Exams
Example 32 Important Deleted for CBSE Board 2022 Exams
Example 33 Important You are here
Example 34 Deleted for CBSE Board 2022 Exams
Example 35 Deleted for CBSE Board 2022 Exams
Example 36 Important
Example 37 Important
Last updated at Feb. 15, 2020 by Teachoo
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)= (π(πΈ3).π(π΄|πΈ3))/(π(πΈ1)π(π΄|πΈ1)+π(πΈ2)π(π΄|πΈ2)+π(πΈ3)π(π΄|πΈ3)+π(πΈ4)π(π΄|πΈ4)) 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 = (ππ’ππππ ππ πππππ )/(πππ‘ππ ππ’ππππ ππ πππππ ππ π‘βπ πππ₯) = 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 = (ππ’ππππ ππ πππππ )/(πππ‘ππ ππ’ππππ ππ πππππ ππ π‘βπ πππ₯) = 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 = (ππ’ππππ ππ πππππ )/(πππ‘ππ ππ’ππππ ππ πππππ ππ π‘βπ πππ₯) = 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 = (ππ’ππππ ππ πππππ )/(πππ‘ππ ππ’ππππ ππ πππππ ππ π‘βπ πππ₯) = 4/13 Putting values in Equation "P(E3|A)"=(π(πΈ3).π(π΄|πΈ3))/(π(πΈ1)π(π΄|πΈ1)+π(πΈ2)π(π΄|πΈ2)+π(πΈ3)π(π΄|πΈ3)+π(πΈ4)π(π΄|πΈ4)) = (1/4 Γ 1/7)/( 1/4 Γ 3/18 + 1/4 Γ 1/4 + 1/4 Γ 1/7 + 1/4 Γ 4/13 ) = (1/28)/( 1/24 + 1/16 + 1/28 + 1/13 ) = (1/28)/( (1/(4 Γ 6) + 1/(4 Γ 4) + 1/(4 Γ 7)) + 1/13) = (1/28)/( ((4 Γ 7 + 6 Γ 7 + 6 Γ 4)/(4 Γ 6 Γ 4 Γ 7)) + 1/13) = (1/28)/((28 + 42 + 24)/(4 Γ 6 Γ 4 Γ 7) + 1/13) = (1/28)/(94/(4 Γ 6 Γ 4 Γ 7) + 1/13) = (1/28)/((94 Γ 13 + 4 Γ 6 Γ 4 Γ 7)/(13 Γ 4 Γ 6 Γ 4 Γ 7) ) = 1/((94 Γ 13 + 4 Γ 6 Γ 4 Γ 7)/(13 Γ 4 Γ 6) ) = (13 Γ 4 Γ 6)/( 94 Γ 13 + 4 Γ 6 Γ 4 Γ 7) = (13 Γ 2 Γ 6)/( 47 Γ 13 + 2 Γ 6 Γ 4 Γ 7) = 156/(611 + 336) = 156/947 = 0.164