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.
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.
By drawing 5 iterations, both HHT and HTT seem to make an appearance 7 times. How is HHT twice as likely to win?
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%
3 Sep 2012