MathDB

Depei is imprisoned by an evil wizard and is coerced to play the following game. Every turn, Depei flips a fair coin. Then, the following events occur in this order:

\bullet

The wizard computes the difference between the total number of heads and the total number of tails Depei has flipped. If that number is greater than or equal to

4

or less than or equal to

-3

, then Depei is vaporized by the wizard.

\bullet

The wizard determines if Depei has flipped at least

10

heads or at least

10

tails. If so, then the wizard releases Depei from the prison. The probability that Depei is released by the evil wizard equals

\frac{m}{2^k}

, where

m, k

are positive integers. Compute

m+k

Problem Statement