Coin Flipping Poll

[Tiberius]

Imagine there's a completely random event with two outcomes, say flipping a coin. Each flip has an equal probability of landing heads or tails. Now imagine that we’re interested in seeing how long it takes to get a certain sequence of outcomes.

Pattern 1: Tails, Heads, Tails

Pattern 2: Tails, Heads, Heads

Now, suppose we flip a coin until Pattern 1 is reached, note how many coin flips it took, and then we repeat the process many times and average how many flips it takes to get a tails-heads-tails sequence. After that, we go through the same process to see how many flips it takes to get Pattern 2, a tails-heads-heads sequence.

So, on average, which pattern takes fewer coin tosses?

[pack3tg0st]

statistically, there isn't a difference.

[Rev. Rye]

Why would there be much of a difference? The odds of heads or tails is always 50/50.

[Eilonnwy]

I said equally in the poll, but I want to change it to pattern 2

[The_Flying_Skeptic]

yeah... there shouldn't be a difference in the likelihood any pattern will arise.

[Tiberius]

I'm keeping my mouth shut. You've all either done very well or very badly, and that's all I'm saying till we get more results.

[Paul the Human]

Tails, heads, heads would happen faster. I'll bet two blue chips and one red chip.

[theVOID]

It's a trick question, with 'Tails, Heads, Heads' You only have to flip the coin once, then just drop it twice for heads.

[Tiberius]

It's not a trick question. The question stated that you flip the coin until each pattern is reached. There are no tricks in this question; you do the flips and work out the average number of flips needed to get to each pattern.

[Zhalentine]

I put THH.

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Since both begin with TH, we'll assume we already have that and we're about to flip the coin for the xth amount of time.

If we want THH, we flip the coin. If it is heads we have THH and we're done. But, if it tails we have the beginning tails in the our sequence of THH, which means we need to flip two consecutive heads.

If we want THT, we flip the coin. If it is tails we got our match, but if it is heads we have to start over and need to flip 3 more coins to try to get THT.

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