MathDB

Every time Josh and Ron tap their screens, one of three emojis appears, each with equal probability: barbecue, bacon, or burger. Josh taps his screen until he gets a sequence of barbecue, bacon, and burger consecutively (in that specific order.) Ron taps his screen until he gets a sequence of three bacons in a row. Let

M

and

N

be the expected number of times Josh and Ron tap their screens, respectively. What is

|M-N|

Problem Statement