A card is drawn at random from a standard deck of cards. Recall that there are 13 hearts, 13 diamonds, 13 spades, and 13 clubs in a standard deck of cards. Let H be the event that a heart is drawn, let R be the event that a red card is drawn let F be the event that a face card is drawn, where the face cards are the kings, queens, and jacks. (a) If I draw a card at random from the deck of 52, what is P(H)? (b) If I draw a card at random, and without showing you the card, I tell you that the card is red, then what are the chances that it is a heart? (c) If I draw a card at random from the deck of 52, what is P(F)? (d) If I draw a card at random, and without showing you the card, I tell you that the card is red, then what are the chances that it is a face card (i.e. what is P(FR))?

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