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

The probability of getting a six is `1/6`
and the probability of not getting a `6` is `5/6`
​
Three cases can be obtain.

Case I:-- If six occurs in the first throw, then the required probability is `1/6`

So,

Amount he will receive =`1`

Case (ii):-- If he does not get a six in the first throw
and gets a six in the second throw, then probability
`=(5/6​xx1/6​)=5/(36)`​

Amount he will receive `=−1+1=0` Rs.

Case(iii):-- If he does not get a six in the first two throws and gets a six in the third throw,
then probability
`=(5/6​xx5/6​xx1/6​)=(25)/(216)​`

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