USAMO Guide Contests

A token is placed at the origin (

x = 0

) of a number line. Each second, it moves 1 unit to the right with a probability of

\frac{1}{2}

, or 1 unit to the left with a probability of

\frac{1}{2}

. The probability that the token reaches

x = 2

before it ever reaches

x = -3

can be expressed as a fraction in simplest form

\frac{m}{n}

. What is the value of

m + n