A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

zarkam21

  • one year ago

You have a 4-card deck containing a king, a queen, a jack, and a 10. You pick a card, keep it, and then pick another card. What is the probability that you pick exactly 1 face card? (Face cards are jacks, queens, and kings.)

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

    There are two ways to accomplish this: choose a face card first and then the 10, or choose the 10 first and then a face card. You need to calculate both of these probabilities and add them together.

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

    So, let's begin. From the 4 cards, what is the probability that a face card will be chosen?

  3. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3/4

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Terrific. You keep that card so now there are only 3 cards. What is the probability that you will then choose the 10?

  5. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1/4

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Not quite. Remember, you kept the first card so, for the second draw, there are only 3 cards? What do you think?

  7. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2/4

  8. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2/3

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Nope. As an example, let's say you drew the queen. Now, what's left in the pack of cards? It's the king, the jack, and the 10. So, what is the probability you draw the 10 from this smaller pack containing only the king, jack, and 10?

  10. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1/3

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Right.

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3/4

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, drawing a face card first had a probability of 1/4 and then drawing the 10 had a probability of 1/3. The probability of these two events happening is the product of these individual probabilities.\[P_{\text{facecard then 10}} = P_{\text{facecard}} \times P_{\text{10}}\]Can you calculate this?

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    * 3/4 sorry

  15. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3/12 which is simplified to 1/4

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Excellent. Now, we have to consider the other possibility.

  17. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    From the pack of 4 cards, what is the probability of choosing the 10 first?

  19. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1/4

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Great. Now, there will be only three cards left: King, queen, jack. What's the probability of choosing a face card from these three?

  21. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3/3

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Terrific. So the probability of these events happening is the product of the two probabilities, just like before. What do you get?

  23. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    same thing :]

  24. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3/12 reduced to 1/4

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's right.

  26. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you !!

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Not done yet.

  28. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh okay

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You've determined that the probability of face card then 10 is 1/4. You've determined that the probability of choosing 10 then face card is also 1/4. These are the only two ways the question can be satisfied. To get the final answer, you need to add these two probabilities together. What do you get?

  30. zarkam21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2/4 which is 1/2

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Good job. Well done.

  32. 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

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.