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Math Help - Not understanding answer...

  1. #1
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    Not understanding answer...

    The question posed is: "Suppose you flip a coin n times. If you win a dollar every time the coin comes up heads and lose a dollar every time it comes up tails, what is the probability that you will win k dollars?"

    The answer given is: "If 2 doesn't divide n + k, the probability is 0. If 2 does divide n + k, the probability is {n \choose \frac {n + k}{2} }"

    Does this make sense to anyone?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by earachefl View Post
    The question posed is: "Suppose you flip a coin n times. If you win a dollar every time the coin comes up heads and lose a dollar every time it comes up tails, what is the probability that you will win k dollars?"

    The answer given is: "If 2 doesn't divide n + k, the probability is 0. If 2 does divide n + k, the probability is {n \choose \frac {n + k}{2} }"

    Does this make sense to anyone?
    To win k dollars requires n1 wins and n2 losses such that n1+n2=n, and
    n1-n2=k.

    This last imples that 2 n1 - (n1+n2) = k, so:

    2 n1 = k+n

    Hence k+n is even so the probabilty of winning k dollars in n trials is 0 if k+n is odd.

    Also if k+n is even then the number of wins is (k+n)/2, and the probability of this is:

    <br />
p(k, n) = {n \choose \frac{k+n}{2}} (1/2)^n<br />

    RonL
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  3. #3
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    So they did leave out part of the answer:
    <br />
(1/2)^n<br />
    which does make sense. Thanks!
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