MathDB

26

Part of 2017 Harvard-MIT Mathematics Tournament

Problems(1)

2017 Guts #26: Kelvin's demise

Source:

2/21/2017
Kelvin the Frog is hopping on a number line (extending to infinity in both directions). Kelvin starts at 00. Every minute, he has a 13\frac{1}{3} chance of moving 11 unit left, a 13\frac{1}{3} chance of moving 11 unit right, and 13\frac{1}{3} chance of getting eaten. Find the expected number of times Kelvin returns to 00 (not including the start) before he gets eaten.
combinatorics