MathDB

In a certain family, a husband and wife made the following agreement: If the wife washes the dishes one day, the husband washes the dishes the next day. However, if the husband washes the dishes one day, then who washes the dishes the next day is decided by drawing a coin. Let

p_n

denote the probability of the event that the husband washes the dishes on the

n

-th day of the contract. Prove that there is a limit

\lim_{n\to \infty} p_n

and calculate it. We assume

p_1 = \frac{1}{2}

Problem Statement