\(20\) men are held captive by a pirate lord, including two friends Jack and Tony.
The pirate decides to set \(10\) of them free. The \(20\) men are randomly divided into \(10\) pairs. Each pair of men then flip a fair coin to decide who goes free.
The probability that both Jack and Tony are set free is \(\frac{A}{B}\) where \(A\) and \(B\) are co-prime positive integers. Find the value of \(A+B.\)
by
Pratik Shastri
