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 You are here
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
Misc 13 Important
Bayes theorem
Last updated at Feb. 15, 2020 by Teachoo
Ex 13.3, 6 There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?Let C1 : two headed coin C2 : biased coin C3 : unbiased coin H : head appears on the coin We need to find Probability that coin is two headed, if it shows head i.e. P(C1|H) P(C1|H) = (π(πΆ_1 ).π(π»|πΆ_1))/(π(πΆ_1 ).π(π»|πΆ_1)+π(πΆ_2 ).π(π»|πΆ_2)+π(πΆ_3 ).π(π»|πΆ_3)) "P(C1)" = Probability that coin selected is two headed = π/π "P(H|C1)" = Probability that head appear on the coin C1 = 1 "P(C2)" = Probability that coin selected is biased = π/π "P(H|C2)" = Probability that head appear on the coin "C2" = 75% = 75/100 = π/π "P(C3)" = Probability that coin selected is unbiased = π/π "P(H|C3)" = Probability that head appear on the coin "C3" = π/π Putting values in formula, P(C1H) = (1/3 Γ 1)/( 1/3 Γ 1 + 1/3 Γ 3/4 + 1/3 Γ 1/2 ) = (1/3 Γ 1)/( 1/3 [1 + 3/4 + 1/2 ] ) = 1/( 9/4 ) = π/π Therefore, required probability is 4/9