BCG Interview Question | Winning

Question

Aman and Akash take turns in rolling a fair six-sided die. Whoever rolls a “6” first wins the game. Akash starts by rolling first.

What’s the probability that Aman wins?

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Dhruv2301 55 years 2 Answers 759 views Great Grand Master 0

Answers ( 2 )

  1. Priyabrata017
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    P(Akash looses)=5/6
    As Akash starts to roll , he has to loose first for Aman to win. It may happen that Akash looses in first roll and Aman wins or Akash and Aman both loose, then Akash loose and Aman wins. This will go on.

    Hence the required Probablity is
    P(Aman wins)=P(Akash looses)*P(Aman wins)+ P(Akash looses)*P(Aman looses)*P(Akash looses)*P(Aman wins) +…
    =5/6*1/6 + 5/6*5/6*5/6*1/6 +….

    Using Infinite GP sum
    we get 5/11.

  2. swap007
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    Probability of getting a six = 1/6
    Probability of not getting a six = 5/6

    The problem takes the form of an infinite Geometric Progression
    5/6*1/6 + 5/6*5/6*5/6*1/6 + 5/6*5/6*5/6*5/6*5/6*1/6 + …………

    sum of infinite G.P is = first term/(1 – common ratio)
    so, probability of Aakash winning is = (5/6)/(1- 25/36) = 5/11

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