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Math Help - [SOLVED] HTHTTH, or HHHTTT ? WHY

  1. #1
    lyssa
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    Post [SOLVED] HTHTTH, or HHHTTT ? WHY

    Which pattern of heads and tails has the highest probability of showing up: (1) HTHTTH, or (2) HHHTTT ?

    Which one (1) or (2)? Why?

    I know that there are 64 possible outcomes, and I believe that the probability is even. I'm not sure why though - both options have three heads, but I don't think that's it. Can you help me understand this?
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  2. #2
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    Quote Originally Posted by lyssa View Post
    Which pattern of heads and tails has the highest probability of showing up: (1) HTHTTH, or (2) HHHTTT ? Which one (1) or (2)? Why?
    Both strings are equally likely (1) HTHTTH, or (2) HHHTTT: \frac {1}{64}.
    Why? Each is a unique string. Each is one in 64.
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  3. #3
    GAMMA Mathematics
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    Quote Originally Posted by Plato View Post
    Both strings are equally likely (1) HTHTTH, or (2) HHHTTT: \frac {1}{64}.
    Why? Each is a unique string. Each is one in 64.
    The coin is unbiased and therefore fair. Flips of tails or heads are just as equally at 50%.

    0.5^6=0.015625

    \left(\frac{1}{2}\right)^6=\frac{1}{64}
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