4 flips of a fair coin

1. Feb 6, 2008

Somefantastik

Given 4 flips of a fair coin, what is the probability of {H,H,H,H}?

I thought since flips of a fair coin are independent, then P(H&H&H&H) = P(H)P(H)P(H)P(H) = 1/(2^4) = 1/16. Am I close?

2. Feb 6, 2008

EnumaElish

Since these are 4 independent trials, yes.

You can verify this & similar problems by figuring out how many ways 4 coins can "land."

3. Feb 6, 2008

Somefantastik

thanks; you're right. I used the tree-notation and got N(ways HHHH)/N(all ways) = 1/16. Thanks again. I'm not entirely sure why that works.

Is it possible to compute the probability that one pattern comes before the other one? Like THHH will happen before HHHH?

4. Feb 6, 2008

chroot

Staff Emeritus
Each of the 16 possible total outcomes (HHHH through TTTT) is equally possible, so there is no way to predict which will occur before another.

- Warren

5. Feb 6, 2008

Somefantastik

Thanks. I should have known that.

6. Feb 7, 2008

CRGreathouse

Remember to distinguish the probability that "THHH" comes before "HHHH" in a series of discrete tuples of four flips from the probability that the subsequence "THHH" comes before "HHHH" in a continuous series of individual flips.