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In a coin tossing game two fair coins are given to two persons X and Y each. The game proceeds until one (or both) of the following happens.

  1. X wins the game if he gets consecutively two tails for the first time.

  2. Y wins the game if he gets a tails immediately followed by a heads for the first time.

Who has the more probability of winning?

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    $\begingroup$ Possible duplicate of Who has more probability of winning the game? $\endgroup$ – lulu Apr 9 at 14:41
  • $\begingroup$ Note: I have retracted my close vote because, on re-reading, the questions are not exact duplicates. In the linked question, the two players were working off a single coin. Here, with two coins, the problem is different. In particular, the answer is obviously not $\frac 12$ each since, if nothing else, there is a possibility of a tie. $\endgroup$ – lulu Apr 9 at 14:49
  • $\begingroup$ Nevertheless, the same techniques apply. Just describe the possible states of the game (there are not many) and look at the possible transitions between the states, $\endgroup$ – lulu Apr 9 at 14:55
  • $\begingroup$ Does each person have one coin or two? In the latter case, does only the last toss of the coins matter (assuming that the coins are tossed "consecutive")? $\endgroup$ – user Apr 9 at 15:00
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The sample space is (HHHH, HHTH, HHHT, HTHH, THHH, TTHH, HTTH, THHT, THTH, HTHT, HHTT, TTTH, HTTT, THTT, TTHT, TTTT). therefore each person has equal possibilities of winning i.e 2/7.

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