MathDB

Ben flips a coin 10 times and then records the absolute difference between the total number of heads and tails he's flipped. He then flips the coin one more time and records the absolute difference between the total number of heads and tails he's flipped. If the probability that the second number he records is greater than the first can be expressed as

\frac{a}{b}

for positive integers

a,b

with

\gcd (a,b) = 1

, then find

a + b

.
Proposed by Vismay Sharan

Problem Statement