Results 1 to 8 of 8
Like Tree2Thanks
  • 1 Post By Milokerr90
  • 1 Post By Soroban

Math Help - combinatorics and coins

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    greece
    Posts
    8

    combinatorics and coins

    If you toss 1000 fair coins 10 times each what is the probability that *some* coin will get 10 heads?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2012
    From
    greece
    Posts
    8

    Re: combinatorics and coins

    answer: aproximatly 63%
    and my question is ..why?

    thnx!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2012
    From
    UK
    Posts
    2
    Thanks
    1

    Re: combinatorics and coins

    The use of *some* coin getting 10 heads suggests that you are interested in the probability that at least one coin gets ten heads.

    If we let N=number of coins getting 10 heads, then Pr(N>=1)=1-Pr(N=0). Therefore, if we can find the probability that none of the 1000 coins get 10 heads, we can calculate your needed answer.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2012
    From
    greece
    Posts
    8

    Re: combinatorics and coins

    I can't see if this problem is easier to get solved.
    Last edited by mathquest; April 8th 2012 at 03:20 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2012
    From
    UK
    Posts
    2
    Thanks
    1

    Re: combinatorics and coins

    If we calculate the probability that one of the 1000 coins does not get 10 heads, then we raise this to the power of 1000 to get the probability that none of the 1000 coins get 10 heads as the events are independent.

    So, one way to find this would be to find the probabilities of getting 1 head, 2 heads,...,9 heads out of 10 and adding these together:

    (1/2)+(1/2)^2+...+(1/2)^9=0.999023438

    Or, we could calculate 1-(Probability of getting 10 heads)=1-(1/2)^10=0.999023438. Now, we raise this to the power of 1000 as we have 1000 coins, and find the probability that none of the 1000 coins get 10 heads=0.999023438^1000=0.376423986, then take this away from 1 to find the probability that at least one gets 10

    1-0.376423986=0.623=62.3%

    This is one of my first replies so please, feel free to ask questions if this isn't clear.
    Thanks from mathquest
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Apr 2012
    From
    greece
    Posts
    8

    Re: combinatorics and coins

    It's very clear solution and explanation! Thank you
    Last edited by mathquest; April 8th 2012 at 03:48 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    772

    Re: combinatorics and coins

    Hello, mathquest!

    My solution is a rehash of Milokerr90's solution . . .


    If you toss 1000 fair coins 10 times each,
    . . what is the probability that some coin will get 10 heads?

    The probability of one coin getting 10 Heads: . \left(\frac{1}{2}\right)^{10} \:=\:\frac{1}{1024}

    The probability of a coin not getting 10 Heads: . 1 - \frac{1}{1024} \:=\:\frac{1023}{1024}

    The probability of 1000 coins, not getting 10 Heads: . \left(\frac{1023}{1024}\right)^{1000}


    The probability of 1000 coins, some getting 10 Heads:

    . . . . 1 - \left(\frac{1023}{1024}\right)^{1000} \;=\;0.623576202 \;\approx\;62.3\%

    Thanks from mathquest
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Apr 2012
    From
    greece
    Posts
    8

    Re: combinatorics and coins

    Thank you Soroban!
    Good rehash!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 12th 2011, 12:15 PM
  2. 9 coins: 7H and 2T
    Posted in the Statistics Forum
    Replies: 5
    Last Post: April 17th 2010, 06:43 PM
  3. Coins
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: July 13th 2009, 01:50 AM
  4. Coins
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 1st 2008, 12:54 AM
  5. coins
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 28th 2008, 06:28 PM

Search Tags


/mathhelpforum @mathhelpforum