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Why is the probability that a fair coin will land the same (all heads or all tails) on $3$ consecutive tosses not $\frac{1}{8}$? Is it not $\left(\frac{1}{2}\right)^3$?

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Because there are two ways it can happen: all heads, all tails, and 1/8+1/8=1/4.

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  • 2
    $\begingroup$ Oh wow.... I can't believe I missed that. $\endgroup$ – John May 9 '13 at 12:24
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TTT $\; \Large\leftarrow$
TTH
THT
THH
HTT
HTH
HHT
HHH $\;\Large\leftarrow$

Sample space size: $8$

"Probability of all heads $\bf OR$ all tails": $\quad P(TTT) + P(HHH) = \dfrac 18 + \dfrac 18 = \dfrac 14$

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  • $\begingroup$ Nice formatting and I'd lose if I had to get either of the endpoints! :-) +1 $\endgroup$ – Amzoti May 10 '13 at 2:37

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