Problem 44503. Anyone for tennis? Your chances of winning a tie-break game
Imagine you are playing tennis and the score has reached 'six games all' in a Tie-break Set, so therefore the next game shall be a 'tie-break game', which is now to be played to decide the outcome of this set. For each point played in the tie-break game your chance of winning is x % (input as a uint8). Given the ITF's scoring system for a "tie-break game" of tennis (excerpted below), please determine your likelihood of winning the tie-break game (output as a single).
Note that as x is taken to be the same for every point in this problem, it does not matter whether you are serving or not.
x = uint8(40) chance = single(0.2125443387076924)
" During a tie-break game, points are scored “Zero”, “1”, “2”, “3”, etc. The first player/team to win seven points wins the “Game” and “Set”, provided there is a margin of two points over the opponent(s). If necessary, the tie-break game shall continue until this margin is achieved. "
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