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JEE Main & Advanced JEE Main Paper (Held On 12-Jan-2019 Evening)

  • question_answer
    In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and lose 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 [JEE Main Online Paper Held On 12-Jan-2019 Evening]

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

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

    C) 0                                 

    D)   \[\frac{400}{3}loss\]

    Correct Answer: C

    Solution :

    Let A =Probability that outcome is 5 or \[6=\frac{1}{3}\] B = Probability that outcome is other than 5 or\[6=\frac{2}{3}\] \[\therefore \]Expected gain/loss \[=A\times 100+BA(-50+100)+{{B}^{2}}A(-50-50+100)\]\[+{{B}^{3}}(-150)\] \[=\frac{1}{3}\times 100+\frac{2}{3}.\frac{1}{3}(50)+\frac{4}{9}.\frac{1}{3}(0)+{{\left( \frac{2}{3} \right)}^{3}}(-150)\] \[=\frac{100}{3}+\frac{100}{9}-\frac{8}{27}\times 150=0\]


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