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Suppose that we draw two cards from a standard deck of 52 playing cards, where ace,...

Suppose that we draw two cards from a standard deck of 52 playing cards, where ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king each appear four times (once in each suit). Suppose that it is equally likely that we draw any card remaining in the deck.

Let X be the value of the first card, where we count aces as 1, jacks as 11, queens as 12, and kings as 13. Let Y be the value of the first card, with the same rules for numerical values. Why is Pr(Y= 13|X= 13) <Pr(Y= 13|X<13)? (You should be able to explain this without calculating the exact values of these probabilities) and then calculate the exact values of Pr(Y= 13|X= 13) and Pr(Y= 13|X<13) and Pr(Y= 13) using the same variables X and Y from the last problem.

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