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Math Help - Another Card Question

  1. #1
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    Another Card Question

    1) Cards are dealt, one at a time, from a standard 52 card deck.
    a) if the first 2 cards are both spades, what is the probability that the next 3 are also spades?

    2) 5 cards are drawn from a standard 52 card deck. What is the probability that all 5 cards will be from the same suit?

    3) A gambler has been dealt 5 cards: 2 are aces, one is a king, one a 5 and one 9. He discards the 5 and 9 and is dealt 2 more cards. What is the probability that he ends up with a full house?

    For 1) all I know is that it's a conditional probability, but I have no clue what values to take

    For 2) is it \frac{4}{2,598,960} since it's \binom{52}{5} and there are 4 possible suits.

    For 3) I'm stuck on the values that I have to pick. Is it \binom{47}{2} = 1081 for the denominator, and \binom{2}{1} \ \binom{3}{1} for the numerator, which equals \frac{6}{1081} ?
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  2. #2
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    Quote Originally Posted by lllll View Post
    1) Cards are dealt, one at a time, from a standard 52 card deck.
    a) if the first 2 cards are both spades, what is the probability that the next 3 are also spades?
    ?
    Two spades dealt, conditional probability next card a spade is 11/50,

    Two spades dealt, conditional probability next two cards are spades is (11/50)(10/49),

    Two spades dealt, conditional probability next three cards are spades is (11/50)(10/49)(9/48).

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by lllll View Post
    2) 5 cards are drawn from a standard 52 card deck. What is the probability that all 5 cards will be from the same suit?
    Probability of 5 spades is (13/52)(12/51)(11/50)(10/49)(9/48)

    as there are 4 suits altogether the probability that all cards are of the same suit is for times this.

    RonL
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by lllll View Post
    3) A gambler has been dealt 5 cards: 2 are aces, one is a king, one a 5 and one 9. He discards the 5 and 9 and is dealt 2 more cards. What is the probability that he ends up with a full house?
    He has 2A and 1K in his hand, he needs to draw either 1A and 1K or 2K to get a full house.

    At this point the remaining deck nominaly has 47 cards of which 2 are A's and 3 are K's

    Take it from there.

    RonL
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