In a game, a person wins 5 rupees for getting a number greater than 4 and loses 1 rupee otherwise, when a fair die is thrown. A man participated in the game, but decided to quit as and when he gets a number greater than 4. Then the expected value (mean value) of the amount he wins/loses is

Step-by-step solution

In a game die is thrown. A man participated in the game, he decided to throw a die thrice but to quit as and when the amount he win/loses is The probability to win in a throw is ( 2 6 ) and loss a throw is ( 4 6 ). Now following cases are possible (i) ( W ) (ii) ( L W ) (iii) L L W (iv) L L L So, the expected value (mean value) of the amount he wins/loses is ( aligned & =5 ( 2 6 )+4 ( 4 6 2 6 )+3 ( 4 6 4 6 2 6 ) +(-3) ( 4 6 4 6 4 6 ) & = 10 6 + 32 36 + 96 216 - 192 216 & = 360+192+96-192 216 = 456 216 = 19 9 aligne