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KVPY Sample Paper KVPY Stream-SX Model Paper-20

  • question_answer
    In a game, a man wins Rs.100 if he gets 5 or 6 on a throw of a fair die and loses Rs.50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is:

    A) \[\frac{400}{9}loss\]

    B) 0

    C) \[\frac{400}{3}gain\]

    D) \[\frac{400}{3}gain\]

    Correct Answer: B

    Solution :

    Let w denotes probability that outcomes 5 or 6
    \[\left( w=\frac{2}{6}=\frac{1}{3} \right)\]
    Let  L denotes probability that outcome 1, 2, 3,4
    \[\left( L=\frac{4}{6}=\frac{2}{3} \right)\]
    Expected Gain/Loss
    \[=w\times 100+Lw(-50+100)+{{L}^{2}}w(-50-50+100)+{{L}^{3}}(-150)\]
    \[=\frac{1}{3}\times 100+\frac{2}{3}.\frac{1}{3}(50)+{{\left( \frac{2}{3} \right)}^{2}}\left( \frac{1}{3} \right)(0)+{{\left( \frac{2}{3} \right)}^{2}}(-150)=0\]


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