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lgbasallote

  • 2 years ago

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?

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  1. satellite73
    • 2 years ago
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    thirteen choose three over fifty two choose three

  2. satellite73
    • 2 years ago
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    times four

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

  4. KingGeorge
    • 2 years ago
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    Try the method I was talking about a little earlier.

  5. KingGeorge
    • 2 years ago
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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.

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

  7. KingGeorge
    • 2 years ago
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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 \[\Large P=\frac{\binom{4}{1}\cdot\binom{13}{3}}{\binom{52}{3}}\]

  8. lgbasallote
    • 2 years ago
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    probability is.... the possible events over the total right?

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

  10. KingGeorge
    • 2 years ago
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    Right.

  11. lgbasallote
    • 2 years ago
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    oh. i get the logic now

  12. lgbasallote
    • 2 years ago
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    thanks

  13. KingGeorge
    • 2 years ago
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    You're welcome.

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