We are given three coins: one has heads in both faces, the second has tails in both faces, and the third has a head in one face and a tail in the other. We choose a coin at random, toss it, and it comes head. What is the probability that the opposite face is tails?

Answer: 0.33Step-by-step explanation:Let, E1 be the coin which has heads in both facesE2 be the coin which has tails in both facesE3 be the coin which has a head in one face and a tail in the other.In this question we are using the Bayes' theorem,where,P(E1) = P(E2) = P(E3) = [tex]\frac{1}{3}[/tex] As there is an equal probability assign for choosing a coin.Given that, it comes up headsso, let A be the event that heads occursthen,P(A/E1) = 1P(A/E2) = 0P(A/E3) =  [tex]\frac{1}{2}[/tex]Now, we have to calculate the probability that the opposite side of coin is tails.that is, P(E3/A) = ?∴ P(E3/A) = [tex]\frac{P(E3)P(A/E3)}{P(E1)P(A/E1) + P(E2)P(A/E2) + P(E3)P(A/E3) }[/tex]= [tex]\frac{(1/3)(1/2)}{(1/3)(1) + 0 + (1/2)(1/3)}[/tex]= [tex]\frac{1}{6}[/tex] × [tex]\frac{6}{3}[/tex]= [tex]\frac{1}{3}[/tex]= 0.3333 ⇒ probability that the opposite face is tails.