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Flipping a coin

  1. Apr 14, 2013 #1
    Flipping a fair coin 10 times. This creates a word of length 10 of the letters C and L. On average how many times it appears in this sub-word CCLLCC?
    C=crown and L= the other side of coin

    i think that if i count CCLLCC in 10 letters of C and L we will have 5 times but how i will find the average?
     
  2. jcsd
  3. Apr 14, 2013 #2

    HallsofIvy

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    If 6 of the letters are "CCLLCC" then the other four letters can be either "C" or "L". There are [itex]2^4= 16[/itex] ways to do that. But you also need to allow for where in the set of 10 letters those letters occur.

    I assume by "sub-word", you require that the letters "CCLLCC" occur together. Do you see that there are 5 places the initial C can be?
     
  4. Apr 14, 2013 #3
    Hello, I'm not quite sure if I'm right as I'm still a novice in the world of math. It's been a while since I have taken my prob/stats class.

    __ __ __ __ __ __ __ __ __ __

    There are 2 ways either C or L for each of the spaces above. So, the total number of ways for spelling out a 10 letter word is 2*2*2*2... = [itex]2^{10}[/itex] = 1024

    There are 5 ways for CCLLCC to occur inside some of the 10 letter words. One of them looks like this:

    C C L L C C __ __ __ __

    The spaces containing CCLLCC are all "locked in". So, there are 4 spaces left for choices.

    2*2*2*2 = [itex]2^{4}[/itex] = 16
    There are 5 ways in which CCLLCC can occur because you can just shift CCLLCC one space to the right each time to get a new word that contains CCLLCC.

    Possible ways of getting a word with CCLLCC in it: 5*16 = 80

    I'm not sure what you meant by "average", so I guess you want the probability as well. [itex]\frac{80}{1024}[/itex] = 0.0781

    Once again I'm not a 100% sure, but I hope it helps you a bit. :P
     
    Last edited: Apr 14, 2013
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