Misc 16 - Chapter 13 Class 12 Probability (Term 2)
Last updated at Feb. 15, 2020 by Teachoo
Bayes theorem
Ex 13.3, 2 Important
Ex 13.3, 3
Misc 3
Ex 13.3, 4 Important
Ex 13.3, 9
Ex 13.3, 5
Ex 13.3, 13 (MCQ) Important
Example 21 Important
Ex 13.3, 6 Important
Ex 13.3, 10 Important
Example 18 Important
Example 17 Important
Ex 13.3, 7
Ex 13.3, 8 Important
Example 19 Important
Ex 13.3, 11
Ex 13.3, 12 Important
Example 37 Important
Example 20 Important
Example 33 Important
Misc 12
Misc 16 Important You are here
Misc 13 Important
Bayes theorem
Misc 16 Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in color. Find the probability that the transferred ball is black. Let A : Event of drawing red ball from Bag II E1 : Event that red ball is transferred from Bag I E2 : Event that black ball is transferred from Bag I We need to find out the probability that the ball transferred is black, if ball drawn is red in color i.e. P(E2|A) P(E2|A) = (π(πΈ_2 ).π(π΄|πΈ_2))/(π(πΈ_1 ).π(π΄|πΈ_1)+π(πΈ_2 ).π(π΄|πΈ_2) ) "P(E1)" = Probability that red ball is transferred from Bag I = 3/7 P(A|E1) = Probability that red ball is drawn from bag II ,if red ball is transferred from Bag I = 5/10 = 1/2 "P(E1)" = Probability that red ball is transferred from Bag I = 3/7 P(A|E1) = Probability that red ball is drawn from bag II ,if red ball is transferred from Bag I = 5/10 = 1/2 "P(E2)" = Probability that black ball is transferred from Bag I = 4/7 P(A|E2) = Probability that red ball is drawn from bag II ,if black ball is transferred from Bag I = 4/10 = 2/5 P(E2|A) = (π(πΈ_2 ).π(π΄|πΈ_2))/(π(πΈ_1 ).π(π΄|πΈ_1)+π(πΈ_2 ).π(π΄|πΈ_2) ) = (4/7 Γ2/5 )/(3/7 Γ1/2 + 4/7 Γ2/5) = (8/35 )/(3/14+ 8/35) = (8/35 )/((15+16)/70 ) = (ππ )/ππ