4. Alice and Bob take turns rolling a fair six sided die. They keep playing this...

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4. Alice and Bob take turns rolling a fair six sided die. They keep playing this game until someone gets a 6, and that person

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Answer 1

Answer #1

P(Alice wins) =P(Alice roll a 6 in first attempt)+P(Alice and Bob do not roll a 6 on first attempt and Alice roll on 2nd)+............

=(1/6)+(5/6)*(5/6)*(1/6)+(5/6)*(5/6)*(5/6)*(5/6)*(1/6)+..............

=(1/6)/(1-(5/6)²) =6/11 =0.5455 ( as sum of infinite geometric series is a/(1-r))

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Answer 2

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