A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

An urn contains six red balls, five white balls, and four black balls. Four balls are drawn from the urn at random without replacement. For each red ball drawn, you win $10, and for each black ball drawn, you lose $15. Let X represent your net winnings. Compute E(X), your expected net winnings.

  • This Question is Closed
  1. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    First you need to find the probabilities for 1, 2, 3 and 4 red balls in a draw of four balls, and the probabilities for 1, 2, 3 and 4 black balls in a draw of four balls. \[\large P(1\ red)=\frac{6C1\times 9C3}{15C4}\] \[\large P(2\ red)=\frac{6C2\times 9C2}{15C4}\] \[\large P(3\ red)=\frac{6C3\times 9C1}{15C4}\] \[P(4\ red)=\frac{6C4}{15C4}\]

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

    what does C represents

  3. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    For example, 9C3 means the number of combinations of 9 different things taken 3 at a time. It can also be read as '9 choose 3'.

  4. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Have you studied combinations?

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

    i haven't studied it yet just studying ahead of class. You getting ready for it. If you could shed some light on it. I would really appreciate it.

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

    in combination so far i know is that order doesn't matter. n!/r! (n-r)!

  7. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Many calculators have the combinations function. Using a suitable calculator the results for the equations that I posted are: P(1 red) = 0.369; P(2 red) = 0.396; P(3 red) = 0.132; P(4 red) = 0.011.

  8. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Now you need to calculate the probabilities of 1, 2, 3 and 4 black balls in a draw of four balls.

  9. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\large P(1\ black)=\frac{4C1\times 11C3}{15C4}\]

  10. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Having found all the required probabilities, each value of red probability is multiplied by $10 and each value of black probability is multiplied by $15 and assigned a negative value. These products are then summed to find the expected value.

  11. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\large E(X)=\sum_{}^{}xp(x)\]

  12. 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.