Pretty standard question that has been asked before... keep flipping a coin until a winning combination appears (either HHT or HTT). Which strategy would you pick given the choice and why. Find the probabilities of winning associated with each strategy.

Question

Sigiloso · Accepted Answer

Essentially HHT is the better strategy. The probabilities are 2/3 HHT and 1/3 HTT.

To see this if you draw a tree diagram (best to draw 4-5 iterations if you can't see it) and look at all the possible ways of winning.  It turns out HHT is twice as likely to win hence the 2/3, 1/3 split.

Sigiloso · Answer

Because you can throw h h h and all you need to throw is a tails to get HHt, but there is no fail, please play again throw for htt, so yes, on a throw of 3, they have th same probability, but in  a continued series you can play again on h h t if you fail on th 3rd throw.

bob · Answer

By drawing 5 iterations, both HHT and HTT seem to make an appearance 7 times. How is HHT twice as likely to win?

Sigiloso · Answer

Note that both HHT and HTT combination starts with H, so you can almost neglect H, so when you  first observe an H, you wait for HT or TT both of which are equally as likely given the order matters i.e. (HT and TH are different), hence both should be good strategies.

anonim · Answer

The mathematical expectation of hte number of flipping for both compbinations is 25/2. In any case the probabilities of appearance of these compbinations are the same, so one can use both strategies with the same result. 50% 50%

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