# A Puzzle in probability theory

Calculating probability for a never ending situation which is recurring.

Problem: A coin tossing game between two friends (of course Alice & Bob may be Eve is also there watching them play).

Find probability of Alice winning if both Alice and Bob has two weighted coins which has `a` and `b`

Assume Alice plays first and whoever gets Head first wins.

Solution:

P(A) = Probability of Alice winning the game = Probability of Alice coin to show head on first throw + (Probability of Alice count to show Tail on first throw)(Probability of Bob coin to show tail)*Probability of Alice count to come head + .. …

``` H + TT H + TT TT H```

``` P(A) = a + (1-a)(1-b) P(A) => P(A) = a / (a(1-b) + b) ```

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