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lgbasallote

Three cards are given to you from a well-shuffled deck of cards. What is the probability that you get all 3 cards from the same suit?

  • one year ago
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  1. satellite73
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    thirteen choose three over fifty two choose three

    • one year ago
  2. satellite73
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    times four

    • one year ago
  3. lgbasallote
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    is this \[\frac 1{52 C3}\]

    • one year ago
  4. KingGeorge
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    Try the method I was talking about a little earlier.

    • one year ago
  5. KingGeorge
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    You first need to find the possible ways you can choose three cards from the same suit, and then divide by all the possible three card hands. So you have Construction: Choices: 1. Choose a suit \(\binom41\) and then 2. Choose a 3 card set from 13 \(\binom{13}{3}\) So there are \[\binom41\cdot\binom{13}{3}\]3card hands where all the cards are from the same suit.

    • one year ago
  6. lgbasallote
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    so the probability would be \[\frac 1{4 C 1 \times 13 C 3}\]

    • one year ago
  7. KingGeorge
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    Now we need to find all 3 card hands total. This is just \(\binom{52}{3}\) (it's a one step process with how I was doing it before). Thus, your probability would be \[\Large P=\frac{\binom{4}{1}\cdot\binom{13}{3}}{\binom{52}{3}}\]

    • one year ago
  8. lgbasallote
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    probability is.... the possible events over the total right?

    • one year ago
  9. KingGeorge
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    We have to divide by the total number of hands to find probability.

    • one year ago
  10. KingGeorge
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    Right.

    • one year ago
  11. lgbasallote
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    oh. i get the logic now

    • one year ago
  12. lgbasallote
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    thanks

    • one year ago
  13. KingGeorge
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    You're welcome.

    • one year ago
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