Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

xEnOnn

  • 2 years ago

Suppose I have 3 dices. I throw them. I want to get a {1,2,5}. So I do this to get the probabilities: \[\frac{1}{6} \cdot \frac{1}{6} \cdot \frac{1}{6} \] In this case, have I considered other combinations like {2, 1, 5}, {5,2,1}, etc?

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

    You have not considered those other cases. You're assuming you get a 1, 2, and 5 in that order.

  2. xEnOnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If I want to consider, what should I do?

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

    You just have to do one more thing. You can just consider all possible orderings. There happen to be \(3!=6\) orderings, and they all have equal probability. Thus, just multiply your original answer by 6.

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

    Suppose if there were repeated values in side it: {2, 2, 5}. Then in this case, would I still multiply by 3!?

  5. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    long story short, no. I'll explain in a minute.

  6. xEnOnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok sure. I will wait for your explanation. Thanks! :)

  7. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Hold on, for your first question, are you throwing all three dice at the same time? Or one a a time?

  8. xEnOnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Wouldn't it be the same? They are all iid.

  9. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    It's actually a little bit different. If we throw them one at a time, we do the process I explained above. Otherwise, you have to do something different.

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

    I think it is all thrown together.

  11. xEnOnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I don't think this is it. Even if they are all thrown together, the dices are i.i.d. random variables on their own.

  12. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    There's a difference between thrown together and thrown at the same time. You get different information about which dice need to which numbers.

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

    hmm... with your second equation, does it count the combinations of it?

  14. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    If we were looking at \(\{2, 2, 5\}\) instead, we have to look at a couple different cases. Drawing a tree is a good idea here. Like above, we have a \(2/6\) chance of getting a 2 or a 5. Then, within this probability, there's a \(2/3\) chance we get a 2, and \(1/3\) chance we get a 5. If we get a 5, we need to find the probability of getting 2 2's, and if we get a 2, we find the probability of getting a 2 and a 5.

  15. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Also, you were correct in thinking I was wrong with my other explanation. It doesn't actually matter. I was merely getting confused.

  16. xEnOnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh I see. Thanks!! :) And just one thing, how do you type the math equations inline? I used the \[ tags but it goes to the next line.

  17. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    use \( instead of \[

  18. xEnOnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ohh...haha...thanks for your help and explanation! :)

  19. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I should note that doing it the other way I suggested is also a valid way of doing it, but you get \[{3 \over 6} \cdot{2 \over 6}\cdot{1 \over 6}={3! \over 6^3}\]Not what I originally got.

  20. xEnOnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks! :)

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.