• 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.
• According to your question, he lands in front of heaven gate. So he just gets in, he ignores other door. Case solved.

or else you have to modify your question.

• Entering the heaver is decided by the person himself while he is alive. That means the more good deeds and good to others, he is sure of going to heaven, other wise hell is confirmed birth for him and no return to heaven. By the way each day behavior of a person is be tabulated by the assistants of Lord Yama who is the final decider on who is going to hell and who is going to heaven and there is no sojourn or short journey as such in heaven. Even the greatest deed doer in life, if err for once, gets deleted from the list of probables to the heaven. Such is the strict guidelines and rules of Dev lok.
K Mohan
Even this challenging situation would ease

• Wow on surface it looks completely unsolvable. I guess I need to use permutations. Why is finding probability so hard!!!
Well broadly speaking, if you wanted to get to heaven in one go, 1/3 is the probability obviously.
If there was no reshuffling he would be successful the third time too ofcourse.
Total no. Of doors=3.
Probability of heaven in first go= 1/3.
Probability of hell= 2/3.
But since the doors are shuffled the total number of doors remain the same.
Now I have to multiply 1/3, x times until my probability is achieved. The question is tough because I don't know how many times he tries. If I know that the question becomes very easy to solve.
If he does thrice the probability, is 1/27.
Ten times, the probability is 1/3^10(impossible in a clear sense).
So the more he tries, more impossible it seems.

I am finding it very hard at this point. But this is what I observed. I'll let a permutations combinations expert to do the rest.

The stronger a light shines the darker are the shadows around it.

• Mr. Aditya Mohan: A very good try. The more he comes back to the main get, the less chance of him entering into heaven.

I could not solve it, and I understand that this is a tough question.

Non-violence is the greatest Dharma; So too is all righteous violence.

• Tough question. Blind answer from me. The probability would be seven times to reach the heaven, if he misses the first opportunity to enter the haven. Sorry, No explanation.
No life without Sun

• I think what Aditya has observed is correct. As the gates get reshuffled every time, each event of entering the heaven is an independent event having the probability of 1/3. So, we keep on multiplying 1/3 x 1/3 x 1/3 x........ and so on, until he reaches the heaven. So, if he has done good deeds on earth, his probability of reaching the heaven is 1/3 and if he has done bad deeds on earth, his probability of reaching the heaven is 0 (1/infinity).

• The person may go to heaven in the first attempt provided he chooses the correct gate. If the gates are randomly shuffled, there is every possibility that he may not reach heaven at all. It all depends on our assumptions. Assuming that the gates are shuffled in a sequence, it will take a maximum of 4 days to reach heaven provided that one particular gate is chosen, for example, the first gate on all the days.
" Be Good and Do Good "

• The information given is not sufficient to calculate mathematically. But we can say he is having 33.3% chance to enter to heaven in first chance itself. Otherwise, everything will be a guesswork only.
drrao
always confident

• So far, I have received seven responses. Out of these seven responses, the responses of Mr. Bhuvan and Mr. Aditya Mohan are most logical.
Non-violence is the greatest Dharma; So too is all righteous violence.