# Probability that a fair coin will land all the same in $3$ consecutive tosses

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 $\left(\frac{1}{2}\right)^3$?

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

• Oh wow.... I can't believe I missed that. – John May 9 '13 at 12:24

TTT $\; \Large\leftarrow$
TTH
THT
THH
HTT
HTH
HHT
HHH $\;\Large\leftarrow$

Sample space size: $8$

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

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