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

N/a

Explanation

In a throw of a dice, probability of getting the number `6=1/6`
and the probability of not getting the number `6=5/6`
So, three possibilities are here.
(i) He obtained the number of first throw then required probability `=1/6` and amount `=Rs. 1`
(ii) If he does not obtain the number 6 in first throw but obtain the number 6 in 2nd throw.
then required probability `=5/6xx1/6=5/36`
and amount received `=Rs. (-1+1)=0`
(iii) If he does not obtain the number 6 in first two throws but obtain the number 6 in 3rd throw then required probability `=5/6xx5/6xx1/6=25/216`
and amount received `=Rs. (-1-1+1)Rs. (-1)`
Therefore expected value of the amount the wins/ loses
`=1/6(1)+(5/6xx1/6)(0)+[(5/6)^(2)xx1/6](-1)`
`=1/6-25/216=(36-25)/216=11/216`