Misc 11 - Chapter 13 Class 12 Probability

Transcript

Misc 11 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. 1st throw : He gets a six P(win) = 1 6 Amount won = 1 2nd throw : He does not get 6 in 1st throw , He gets six in 2nd throw So, P(win) = 5 6 1 6 = 5 36 Amount won = 1 + 1 = 0 3nd throw : He does not get 6 in 1st throw , He does not get 6 in 2nd throw ,He gets six in 3rd throw So, P(win) = 5 6 5 6 1 6 = 25 216 Amount won = 1 1 + 1 = 1 Expected Value = Amount won Probability for all three throws = (1 ) + (0 ) + ( 1 ) = 1 6 + 0 25 216 = 1 6 25 216 = 36 25 216 =