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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 23 A and B throw a die alternatively till one of them gets a ‘6’ and wins the game. Find their respective probabilities of winning, if A starts first.Winning the game is getting a 6 on the die P(getting 6) = 1/6 P(not getting six) = 1 – P(getting six) = 1 – 1/6 = 5/6 1st throw by A: A gets a six P(A wins) = 𝟏/𝟔 2nd throw by B: A does not get 6, B gets six So, P(B wins) = 𝟓/𝟔 × 𝟏/𝟔 3rd throw by A: A does not get 6, B does not get 6, A gets six P(A wins) = 𝟓/𝟔 × 𝟓/𝟔 × 𝟏/𝟔 4th throw by B: A does not get 6, B does not get 6, A does not get 6, B gets six P(B wins) = 𝟓/𝟔 × 𝟓/𝟔 × 𝟓/𝟔 × 𝟏/𝟔 5th throw by A: A does not get 6, B does not get 6, A does not get 6, B does not get 6, A gets six P(A wins) = 𝟓/𝟔 × 𝟓/𝟔 × 𝟓/𝟔 × 𝟓/𝟔 × 𝟏/𝟔 and so on So, probability that A wins is P(A wins) = 1/6 + 5/6 × 5/6 × 1/6 + 5/6 × 5/6 × 5/6 × 5/6 × 1/6 + ……. = (1/6) + (5/6)^2 (1/6) + (5/6)^4 (1/6) + ............ = (𝟏/𝟔)/(𝟏 − (𝟓/𝟔)^𝟐 ) = (1/6)/(1 − 25/36) = (1/6)/((36 − 25)/36) = (1/6)/(11/36) = 6/11 ∴ P(A wins) = 𝟔/𝟏𝟏 and P(B wins) = 1 – P(A wins) = 1 – 6/11 = 𝟓/𝟏𝟏

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.