Ex 13.3, 6

Transcript

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 the Probability that the coin is two headed, if it shows head i.e. P(C1|H) P(C1|H) = 𝑃 𝐶﷮1﷯﷯.𝑃(𝐻| 𝐶﷮1﷯)﷮𝑃 𝐶﷮1﷯﷯.𝑃(𝐻| 𝐶﷮1﷯)+𝑃 𝐶﷮2﷯﷯.𝑃(𝐻| 𝐶﷮2﷯)+𝑃 𝐶﷮3﷯﷯.𝑃(𝐻| 𝐶﷮3﷯)﷯ Putting values in formula, P(C1H) = 1﷮3﷯ × 1﷮ 1﷮3﷯ × 1 + 1﷮3﷯ × 3﷮4﷯ + 1﷮3﷯ × 1﷮2﷯ ﷯ = 1﷮3﷯ × 1﷮ 1﷮3﷯ [1 + 3﷮4﷯ + 1﷮2﷯ ] ﷯ = 1﷮ 9﷮4﷯ ﷯ = 𝟒﷮𝟗﷯ Therefore, required probability is 4﷮9﷯