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Sample spaces having equally likely outcomes

  1. Mar 16, 2013 #1
    If we flip a coin n-times,
    what is the probability of the event $$A= \left \{there \space are \space k \space head \right \}$$.
    I should find the number of elements of A,
    the book says that is $$\binom{n}{k}$$ but for $$n=3$$ and $$k=2$$, all the possible outcomes are:
    $$A= \left \{(h, h,h), (h, h, x), (h, x, h), (x, h, h) \right \}$$, where the position of h or x is the k-flip.
    How to find this number?

    PS. h is head.
     
    Last edited: Mar 16, 2013
  2. jcsd
  3. Mar 16, 2013 #2

    tiny-tim

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    hi blob84! :smile:

    i'm sorry, i don't understand this at all :redface:

    your example seems to be k = 3, not n = 3, and i don't understand what those four outcomes are :confused:

    can you explain again?​
     
  4. Mar 16, 2013 #3
    k is the number of the head in A, int the example k = 2, any vector of A has at least two head.
    you flip a coin n-times, so if n = 3 you flip the coin 3 times, the problem is to count the number of vectors in A.

    PS. h is head.
     
    Last edited: Mar 16, 2013
  5. Mar 16, 2013 #4

    tiny-tim

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    ah, now i see what you meant :smile:

    no, if k = 2, there must be exactly 2 heads

    so the possible outcomes are

    1: xxx k = 0 (0 heads)

    3: xxh xhx hxx k = 1 (1 head)

    3: xhh hxh hhx k = 2 (2 heads)

    1: hhh k = 3 (3 heads)​
     
  6. Mar 16, 2013 #5
    yes only 2 head, oh my god!
    Thanks.
     
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