# Thread: [SOLVED] HTHTTH, or HHHTTT ? WHY

1. ## [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?

2. Originally Posted by lyssa
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.

3. Originally Posted by Plato
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%.

$0.5^6=0.015625$

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