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# Two cards are drawn at random from a standard deck. (A standard deck has 52 cards: 13 hearts, 13 diamonds, 13 clubs, and 13 spades.) (a) Are the outcomes of drawing the two cards independent? Why? (b) If the first card is replaced before the second is drawn, what is the probability that both cards will be hearts? (c) If the first card is not replaced before the second is drawn, what is the probability that both cards will be hearts?

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(a) Two events are independent, if the probability that one event occurs in no way affects the probability of the other event occurring.

Drawing two cards is NOT INDEPENDENT when you do NOT replace the first card after drawing it, because after drawing the first card, there will be one less card in the deck of cards and thus the probability for the second card is different than the probability for the first card.

Drawing two cards is INDEPENDENT when you DO replace the first card after drawing it, because the same cards will be in the deck when drawing the second card as there were when drawing the first card.

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