Marcus and Allen are playing Rock/Paper/Scissors. The first one to one 10 times does not have to do the dishes. The score is now 9 to 7 in favor of Marcus. If ties are ignored and not counted, what is the probabilty Marcus will not have to do the dishes? Express your answer as a common fraction.
Ad the following probabilities (ties not counted):
Marcus wins next
Marcus loses and then wins second decision
Marcus loses twice and then wins third decision.
1/2 + 1/2^2 + 1/2^3
= (12 + 6 + 3)/24
= 7/8