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Mathematics, 11.03.2021 14:00 brittanypelleri5151

A standard deck of 52 playing cards contains 4 suits (hearts, diamonds, clubs, and spades), and each suit contains 13 cards labeled 2 through 10, as well as jack, queen, king, and ace. Sally is dealt a hand of 5 cards. Her first three cards are the 3 of clubs, the 5 of clubs, and the 7 of clubs.

What is the probability that the next two cards she is dealt are the 4 of clubs and the 6 of clubs?

(Assume the following: Sally is the only person receiving cards in this situation, the deck is randomized, and all 52 cards are included.)

Select the explanation that is completely correct.

A. Dealing the next two cards is a dependent event. Since Sally has already been dealt 3 cards, there are 49 cards left in the deck. Only 1 of those cards is the 4 of clubs, and only 1 of those cards is the 6 of clubs. Therefore, Sally has a 149(148)=12352 chance of being dealt those two cards next.
B. Dealing the next two cards is an independent event. Since Sally has already been dealt 3 cards, there are 49 cards left in the deck. There are 13 clubs in the deck, so she has a (1349)(1349)=1692401 chance of being dealt the 4 of clubs and the 6 of clubs next.
C. Dealing the next two cards is an dependent event. Since Sally has already been dealt 3 cards, there are 49 cards left in the deck. There are 13 clubs in the deck, so she has a 1349(1248)=13196 chance of being dealt the 4 of clubs and the 6 of clubs next.
D. Dealing the next two cards is an independent event. Since Sally has already been dealt 3 cards, there are 49 cards left in the deck. Only 1 of those cards is the 4 of clubs, and only 1 of those cards is the 6 of clubs. Therefore, Sally has a 149(149)=12401 chance of being dealt those two cards next.

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