Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

lgbasallote

  • 3 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?

  • This Question is Closed
  1. anonymous
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thirteen choose three over fifty two choose three

  2. anonymous
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    times four

  3. lgbasallote
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is this \[\frac 1{52 C3}\]

  4. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Try the method I was talking about a little earlier.

  5. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so the probability would be \[\frac 1{4 C 1 \times 13 C 3}\]

  7. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    probability is.... the possible events over the total right?

  9. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We have to divide by the total number of hands to find probability.

  10. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Right.

  11. lgbasallote
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh. i get the logic now

  12. lgbasallote
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks

  13. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're welcome.

  14. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy