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Last updated at Feb. 15, 2020 by Teachoo

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.There will be 4 cases He gets 6 in first throw He does not get 6 in 1st throw , He gets six in 2nd throw He does not get 6 in 1st throw , He does not get 6 in 2nd throw, He gets six in 3rd throw He does not get 6 in 1st throw , 2nd throw or 3rd throw Case 1 He gets a six Probability = 1/6 Amount won = 1 Case 2 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 Case 3 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 Case 4 He does not get 6 in 1st throw , 2nd throw or 3rd throw So, P(win) = 5/6 × 5/6 × 5/6 = 125/216 Amount won = –1 – 1 − 1 = –3 Expected Value = Amount won × Probability for all four throws = (𝟏×𝟏/𝟔) + (𝟎×𝟓/𝟑𝟔) + (−𝟏×𝟐𝟓/𝟐𝟏𝟔) + (−𝟑×𝟏𝟐𝟓/𝟐𝟏𝟔) = 1/6 + 0 – 25/216 – 375/216 = 1/6 – 25/216 – 375/216 = (36 − 25 − 375)/216 = (36 − 400)/216 = (−364)/216 = (−𝟗𝟏)/𝟓𝟒

Miscellaneous

Misc 1

Misc 2 Important

Misc 3

Misc 4 Not in Syllabus - CBSE Exams 2021

Misc 5 Important Not in Syllabus - CBSE Exams 2021

Misc 6 Important Not in Syllabus - CBSE Exams 2021

Misc 7 Important

Misc 8 Important

Misc 9 Important Not in Syllabus - CBSE Exams 2021

Misc 10 Important

Misc 11 Important You are here

Misc 12

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18

Misc 19

Chapter 13 Class 12 Probability

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.