MathDB

Siva has the following expression, which is missing operations:

\frac12 \,\, \_ \,\,\frac14 \,\, \_ \,\, \frac18 \,\, \_ \,\,\frac{1}{16} \,\, \_ \,\,\frac{1}{32}.

For each blank, he flips a fair coin: if it comes up heads, he fills it with a plus, and if it comes up tails, he fills it with a minus. Afterwards, he computes the value of the expression. He then repeats the entire process with a new set of coinflips and operations. If the probability that the positive difference between his computed values is greater than

\frac12

can be expressed as

\frac{a}{b}

for relatively prime positive integers

a

b

, then find

a + b

Problem Statement