In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins / loses.

Explanation

In a throw of a die, the probability of getting a six is 1/6​ and the probability of not getting a 6 is 5/6

So we can get three cases


i. If he gets a six in the first throw, so the required probability is 1/6

Amount he will receive =1 Rs

ii. If he gets a six in the second throw, then probability =`(5/6*1/6​)=5/36`

Amount he will receive =−1+1=0 Rs.

iii. If he get a six in the third throw, then probability =`(5/6×5/6​×1/6​)=25/216`

...