Question

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.

Answer 1

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.

Three cases can occur.

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

The amount he will receive = Re 1

ii. If he does not get a six in the first throw and gets a six in the second throw, then