Results 1 to 3 of 3

Math Help - Bucket/ Coin probability question

  1. #1
    Newbie
    Joined
    Sep 2005
    Posts
    11

    Cool Bucket/ Coin probability question

    There is a bucket containing 1000 coins.
    1 of those coins has heads on both sides.
    The other 999 are normal coins with heads and tails.

    I pick one coin from random out of the bucket.
    I flip this coin 10 times and receive heads every time.

    What is the probability that the coin I picked was the coin with heads on both sides?




    I know the answer works out to roughly a half but I don't know how to work it out... any help?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2005
    Posts
    11
    Quote Originally Posted by emydawn View Post
    There is a bucket containing 1000 coins.
    1 of those coins has heads on both sides.
    The other 999 are normal coins with heads and tails.

    I pick one coin from random out of the bucket.
    I flip this coin 10 times and receive heads every time.

    What is the probability that the coin I picked was the coin with heads on both sides?




    I know the answer works out to roughly a half but I don't know how to work it out... any help?

    Thanks

    Couldnt find the delete button but I typically worked it out just as I posted it, so dont worry about replying, but if youre interested, here's how it's done!



    right so ive picked the coin, and its flipped heads 10 times in a row. therefore there are two situations that have happened.

    1) ive picked a regular coin which has just happened to flip heads 10 times in a row

    OR

    2) ive picked the funny coin which will always flip heads anyway


    so one of those situations has definitely happened. therefore u find those probabilities which work out to the following

    1) ive picked a regular coin which has just happened to flip heads 10 times in a row
    =999/1000 * 1/1024 = 0.000976

    2) ive picked the funny coin which will always flip heads anyway
    =0.001


    sum the probabilities

    which gives 0.001976

    then i want the probaability that i DID pick the funny coin, which was 0.001


    therefore the answer is 0.001 / 0.001976

    which gives 0.506179

    ta da
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Exactly. You beat me to the punch. Glad you figured it out.

    This is Bayes Theorem.

    P(A|B)=\frac{P(A)P(B|A)}{P(A)P(B|A)+P(A')P(B|A')}

    If we let A=the probability of getting the fake coin and B = the probability of getting 10 heads in a row, then:

    \frac{(\frac{1}{1000})(1)}{(\frac{1}{1000})(1)+(\f  rac{999}{1000})(\frac{1}{1024})}=\frac{1024}{2023}  \approx{0.5062}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. coin probability
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: February 21st 2010, 09:47 AM
  2. even and odd probability of coin
    Posted in the Statistics Forum
    Replies: 1
    Last Post: January 24th 2010, 03:33 PM
  3. Probability Question regarding tossing of a coin
    Posted in the Statistics Forum
    Replies: 8
    Last Post: December 18th 2009, 07:11 PM
  4. Probability Coin Question
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 17th 2009, 11:49 PM
  5. coin probability
    Posted in the Statistics Forum
    Replies: 5
    Last Post: May 13th 2008, 03:11 AM

Search Tags


/mathhelpforum @mathhelpforum