Question

If you were given a fair coin, and you were to flip it three times and if you were to flip the coin repeatedly until the permutation sequence(where order matters) {HTT} or {HHT} show up, what is the probability to see {HTT} show up first? Show steps to what led to this probability. (Discrete Mathematics)

Thank you

Answer 1

The objective here is to find the probability that {HTT} show up before {HHT}.

Note that both the above events will only occur ( and will must occur) if a toss shows up a head and the secod toss after that shows a tails.

So let us assume that a head occured in one toss and the second toss after that was a tails.

Then, the toss in between the above two will determine which event {HTT} or {HHT} shows up first.

If a tail occured in that toss in between, we can say that {HTT} shows up first.

Thus, probability of getting a tail in that toss will be the probability of {HTT} showing up first

Probability of getting a tails in that toss is as usually . (as the coin is fair)

Therefore probability to see {HTT} show up first is .

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