Misc 11

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 × 𝟏﷮𝟔﷯) + (0 × 𝟓﷮𝟑𝟔﷯) + (–1 × 𝟐𝟓﷮𝟐𝟏𝟔﷯) = 1﷮6﷯ + 0 – 25﷮216﷯ = 1﷮6﷯ – 25﷮216﷯ = 36 − 25﷮216﷯ = 𝟏𝟏﷮𝟐𝟏𝟔﷯