Amanda dies and reaches at the gate of heaven. She has three doors in front of her out of which only one of them leads to heaven. Out of the other two gates, one leads to hell for one day and then back to the gate and one leads to hell for two days and then back to the gate. If she chooses one of these two gates, the gates are shuffled when she returns back.
How long will Amanda take to reach heaven?
Let us simplify the question and then it will lead us to the answer easily. There are three possibilities. Thus the probability of choosing any door is 1/3rd. 1/3 of the time the door to heaven will be chosen by Amanda and thus 1/3 of the time it will take her zero days. 1/3 of the time, the day which leads to hell for one day will be chosen and of those the right door will be chosen the next day. So 1/9 trips take one day. In the similar manner, 1/9 will take to the door which takes to 2 days hell.
When that happens, the cases will be split again and again. Thus on average, it will take three days for Amanda to reach Heaven by choosing the right gate.