Pearls in the box Pearls in the box
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To start the game, they put several black and white pearls in one of the boxes. Each robots have Nth moves, then initial set are restored for a next player. For each move, the robot take a pearl out of the box and put one of the opposite color back. The winner is the one who pulls the white pearl on the Nth step (or +1 point if they play many parties).

Our robots don't like indeterminacy and want to know the probability of a white pearl on the Nth step. The probability is a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The result is a float from 0 to 1 with two digits precision (±0.01).

You are given a start set of pearls as a string that contains "b" (black) and "w" (white) and the number of the step (N). The order of the pearls does not matter.


Input: The start sequence of the pearls as a string and the step number as an integer.

Output: The probability for a white pearl as a float.


checkio('bbw', 3) == 0.48
checkio('wwb', 3) == 0.52
checkio('www', 3) == 0.56
checkio('bbbb', 1) == 0
checkio('wwbb', 4) == 0.5
checkio('bwbwbwb', 5) == 0.48

How it is used: This task introduces you to the basics of probability theory and statistics. Fun fact: regardless of the initial state, as the number of steps increases, the probability approaches 0.5!

Precondition: 0 < N ≤ 20
0 < |pearls| ≤ 20

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