Two cards are drawn at random from a standard deck of cards without replacement. Determine the probability that: a) Both are black b) Both are aces c) The first is a three and the second is a jack d) At least one of them is a face card

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Probability first card (black) = 26/52 or 1/2; probability second card (black) = 25/51   (you have to change the denominator because you did not replace your original pulled card which forces the deck to have fewer cards available for the second pull.)  This is true of the following scenarios as well.  

so Probability (black and black) = 1/2 * 25/51 = 25/102 (.245098039)

Probability first card (Ace) = 4/52 or 1/13; probability second card (ace) 3/51

so Probability (Ace and Ace) = 1/13 * 3/51 = 3/663 or 1/221 (.004524887)

Probability (three) = 4/52 or 1/13 and Probability (jack) = 4/51 

so probability (three and jack) = 1/13 * 4/51 = 4/663 (.006033183)

Probability (at least one card is face card) 16/52 = 4/13   That would be the probability on your first pull.  If your first pull is not a face card, then the new probability would be 16/51.  

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