# When will he finally enter the heaven?

The following is a terribly tough question for me:-A person dies and arrives at the gate of heaven. There are three doors; one of them leads to heaven. another one leads to a one day stay at hell, and then back to the gate, and the third gate leads to a two days stay at hell, and then back to the main gate. Every time the person is back to the gate, the three doors get reshuffled. How long will it take the person to finally reach the heaven?

This is a question on probability theory and I could not solve it. Can anybody help me? Please give a detailed reasoning.