1. This site uses cookies. By continuing to use this site, you are agreeing to our use of cookies. Learn More.
  2. Hi Guest, welcome to the TES Community!

    Connect with like-minded professionals and have your say on the issues that matter to you.

    Don't forget to look at the how to guide.

    Dismiss Notice

Probability Question

Discussion in 'Mathematics' started by 1033, Jan 27, 2011.

  1. A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up or face down. The total value of the cards which landed face up is then calculated. (Card values are assigned as follows: Ace=1, 2=2, ... , 10=10, Jack=11, Queen=12, King=13. There are no jokers.)



    What is the probability that the total value is divisible by 13?
     
  2. A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up or face down. The total value of the cards which landed face up is then calculated. (Card values are assigned as follows: Ace=1, 2=2, ... , 10=10, Jack=11, Queen=12, King=13. There are no jokers.)



    What is the probability that the total value is divisible by 13?
     
  3. DM

    DM New commenter

    What have you done so far? It is no coincidence that 13 is prime.
     
  4. erm - is this a project? competetion entry? challenge to us?
     
  5. just a random challenge to the maths forum...





    Was looking for a fun maths problem to do, haven't done it myself yet as i'm trying to plan tomorrow's lessons!
     
  6. what year/ability group were you thinking of aiming it at?
     


  7. the other teachers in my department :) studentwise - depends on how long it takes us to answer!
     
  8. GodOfBiscuits

    GodOfBiscuits New commenter

    As a starting point, the number of combinations of how the cards lie is going to be 2^52 = 4.5E15

    All we need to do now is try every combination to see if it matches any one of the 28 multiples of 13 we can get from the cards.

    It's gonna be a long night.....



     
  9. I'll start us off:
    K
    KK
    KKK
    KKKK
    QA
    QAQA
    QAQAQA
    QAQAQAQA
    J2
    J2J2
    J2J2J2
    J2J2J2J2
    10 3
    10 3 10 3
    10 3 10 3 10 3
    10 3 10 3 10 3 10 3
    9 4
    9 4 9 4
    9 4 9 4 9 4
    9 4 9 4 9 4 9 4
    8 5
    8 5 8 5
    8 5 8 5 8 5
    8 5 8 5 8 5 8 5
    7 6
    7 6 7 6
    7 6 7 6 7 6
    7 6 7 6 7 6 7 6
    K Q A
    K J 2
    K 10 3

    well, it is more interesting than the washing up...
     
  10. DM

    DM New commenter

    KKK?
    I knew it was only a matter of time before people with flaming torches turned up.
     
  11. This discussion may put me off playing pyramid solitair
     
  12. have you seen the pyramid rubiks cube?
    (oh - going off topic - what will the topic police say?)
     
  13. GodOfBiscuits

    GodOfBiscuits New commenter

    to make matters more complex,
    K
    is really K hearts, K spades, K clubs, K diamonds
    QA is Qh,Ah Qh,As Qh,Ac Qh,Ad
    Qs,Ah Qs,As Qs,Ac Qs,Ad
    Qc,Ah Qc,As Qc,Ac Qc,Ad
    Qd,Ah Qd,As Qd,Ac Qd,Ad

     
  14. I would say that is fine ... as long as you aren't planning to post lots of faeces that subsequently gets the thread pulled!
     
  15. What shape is it?
     
  16. Erm, what about if we multiplied each unique type-of-card-combination (i.e. KQA but not KK) by 4^n where n is the number of cards - does that help at all?*
    [​IMG] @ DM

    * Be gentle with me if that is complete garbage - I have a splitting headache and should probably have gone to bed an hour ago.


     
  17. DM

    DM New commenter

    Re: your headache:
    Why are there no painkillers in the jungle?













    Because the parrots eat 'em all.
     
  18. GodOfBiscuits

    GodOfBiscuits New commenter

    Multiplying by 4^n does help with the unique combos, but there's a lot more more combos that use multiple cards than use four unique ones.

    6,6,A
    6,3,3,A
    6,2,2,2,A
    6,5,A,A
    6,3,2,A,A
    6,4,A,A,A
    6,2,2,A,A,A
    6,3,A,A,A,A


     
  19. DM - [​IMG] I shall have to remember that one.

    Does order matter?
    i.e.are we counting 6h6sAh as different to
    6s6hAh?

    'cos could we use nCr or nPr to help?

     

Share This Page