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Math Help - When is a fair coin toss not fair?

  1. #1
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    When is a fair coin toss not fair?

    Here's a real twister. I'm not sure if I'm overthinking it?

    A fair coin is tossed 6 independent times with the result of 4 heads and 2 tails. What was the most likely number of heads after the first 4 tosses?

    Now, I'm not sure if this is a trick question, and the right answer is just 2, or if I need to take into consideration that the probability of a heads in these first 6 tosses is 4 out of 6 - or is it still 1 out of two?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ScienceGeniusGirl View Post
    Here's a real twister. I'm not sure if I'm overthinking it?

    A fair coin is tossed 6 independent times with the result of 4 heads and 2 tails. What was the most likely number of heads after the first 4 tosses?

    Now, I'm not sure if this is a trick question, and the right answer is just 2, or if I need to take into consideration that the probability of a heads in these first 6 tosses is 4 out of 6 - or is it still 1 out of two?
    You are told apriori that the coin is fair.

    You are being asked to find the number N of heads in the first four throws that has maximum probability, given that there are 4 head in the first 6 tosses.

    CB
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  3. #3
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    How would I go about that?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by ScienceGeniusGirl View Post
    How would I go about that?
    One way:

    List all sequences of 6 tosses with 4 heads and 2 tails.

    there are 15.

    Of these 6 have 2 heads in the first 4 tosses, 8 have 3 heads in the first 4 tosses, and 1 has all heads in the first 4 tosses.

    CB
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