Determine the conditional probability

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On your way home after a late night of studying Bayes' rule you come across a mysterious hooded figure standing behind a table displaying two coins and two urns. You are told the first urn contains 5 cards from the suit of diamonds and 3 from the suit of clubs and that the second urn contains 6 diamonds and 2 clubs. Furthermore, you are instructed to flip both coins and if this does not result in any heads you must select a card at random from the first urn, otherwise you must choose a card from the second urn. "This is the dumbest game I have ever heard of" you tell the hooded figure. Dejected the person behind the table offers you a chance to win a prize. If you correctly determine the conditional probability that a randomly selected card came from the first urn, given that it is a club, you get to keep both coins. What is this probability?

Reference no: EM132858289

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