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  1. MHB Apprentice

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    #1
    the probability of getting a head on flipping a biased coin is p. the coin is flipped n times producing a sequence containing m heads and (n-m) tails what is the probability of obtaining this sequence from n flips.
    i cant understand the wording

  2. Pessimist Singularitarian
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    #2
    I've moved this thread since our advanced forum is for calculus based stats.

    A few things we need to observe:

    The probability of getting heads is:

    $ \displaystyle P(H)=p$

    Now, we know that it is certain that we will either get heads or tails, so we may state:

    $ \displaystyle P(H)+P(T)=1\implies P(T)=1-P(H)=1-p$

    So, the probability of getting $m$ heads is:

    $ \displaystyle P\left(H_m\right)=p^m$

    And the probability of getting $n-m$ tails is:

    $ \displaystyle P\left(T_{n-m}\right)=(1-p)^{n-m}$

    Next we need to look at the number $N$ of ways to choose $m$ from $n$:

    $ \displaystyle N={n \choose m}$

    Can you put all this together to find the requested probability?

  3. MHB Apprentice

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    #3 Thread Author
    when i put this all together i get (n ncr m)*p*(1-p)^n-m however at the back of the book it says the answer is p^m(1-p)^n-m

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    #4
    What I get is:

    $ \displaystyle P(X)={n \choose m}p^m(1-p)^{n-m}$

    And this agrees with the binomial probability formula.

    This is the probability of getting any sequence with $m$ heads, for any particular such sequence, then it would be:

    $ \displaystyle P(X)=p^m(1-p)^{n-m}$

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    #5
    Quote Originally Posted by markosheehan View Post
    when i put this all together i get (n ncr m)*p*(1-p)^n-m however at the back of the book it says the answer is p^m(1-p)^n-m
    Was it possible that the problem asked for the probability of m heads in a row followed by n-m tails in a row? As MarkFl said, that probability if for any particular such sequence- "m heads in a row followed by n- m tails in a row" or "n- m tails in a row followed by m heads in a row" or "A head, then a tail, then a head, followed by m- 2 heads in a row, followed by n- m- 1 tails in a row", etc.

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