Results 1 to 3 of 3

Math Help - Probability of a tail followed by 2 heads on a biased coin

  1. #1
    Newbie
    Joined
    Feb 2013
    From
    US
    Posts
    12

    Probability of a tail followed by 2 heads on a biased coin

    Suppose we have a biased coin for which the probability of heads is 3/4 while the probability of tails is 1/4 . What is the probability of a tail followed by 2 heads on three flips of the coin?

    Here is what I have so far: There are 2^3 possible outcomes {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}, and only one way to get THH. I've hit a wall and any pointers would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1

    Re: Probability of a tail followed by 2 heads on a biased coin

    Quote Originally Posted by battery88 View Post
    Suppose we have a biased coin for which the probability of heads is 3/4 while the probability of tails is 1/4 . What is the probability of a tail followed by 2 heads on three flips of the coin?
    If you were to look up the answer in the 'back-of-the-book' it would be:
    \frac{3}{2^6}.

    Now if you can explain to yourself WHY? or HOW? then you will understand.

    HINT: TTH is one out of eight which is a power of two.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,540
    Thanks
    1393

    Re: Probability of a tail followed by 2 heads on a biased coin

    Quote Originally Posted by battery88 View Post
    Suppose we have a biased coin for which the probability of heads is 3/4 while the probability of tails is 1/4 . What is the probability of a tail followed by 2 heads on three flips of the coin?

    Here is what I have so far: There are 2^3 possible outcomes {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}, and only one way to get THH. I've hit a wall and any pointers would be appreciated.
    The probability that the first coin is tails is 1/4. The probability that the second coin is heads 3/4. The probability that the third coin is heads is 3/4. The probability of three independent results, ABC, happening is P(A)P(B)P(C).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability mass function, biased coin
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: September 18th 2011, 02:54 PM
  2. Biased coin
    Posted in the Statistics Forum
    Replies: 3
    Last Post: March 18th 2011, 10:56 PM
  3. Biased Coin Toss
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 12th 2010, 02:35 PM
  4. confidence bounds for two biased coins being heads.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 27th 2010, 11:53 PM
  5. Biased coin
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: September 18th 2009, 01:28 PM

Search Tags


/mathhelpforum @mathhelpforum