What's your expectation
A person gives you a dice and says you to roll it. If you throw a six you get six rupees and the game stops. However if you throw any thing other than six, you get money as the dice indicates and a chance to roll the dice again. It would continue till i throw a six and then I would get rupees 6 and the game would stop and I would collect the money and take it home. For example I roll 2 in first chance than I will get two rupees and a chance to roll the dice again. Then i rolled dice and got 5. Then i will get 5 rupees more and an another chance to roll the dice. Now I threwa six and hence the game ends and i take rupees 13 and go home. What is the expected amount you would win?
Assumptions Dice is fair.
The answer is 21.
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Assume the expected value is x. Once one rolls a number that isn't six their expected value is that number plus x, and if one rolls six then the expected value is just six. Thus x=5/6(x)+1/6(1+2+3+4+5)+1, solving this shows that x=21.