JEE PYQ: Permutation And Combination Question 46
Question 46 - 2019 (12 Jan Shift 1)
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:
(1) $\frac{400}{9}$ loss
(2) $0$
(3) $\frac{400}{3}$ gain
(4) $\frac{400}{3}$ loss
Show Answer
Answer: (2)
Solution
$P(\text{success}) = \frac{1}{3}$, $P(\text{fail}) = \frac{2}{3}$. Expected value $= \frac{1}{3}(100) + \frac{2}{9}(50) + \frac{4}{27}(0) + \frac{8}{27}(-150)$. Calculating: $= \frac{100}{3} + \frac{2}{9} \times 50 + \frac{4}{27} \times 0 + \frac{8}{27}(-150) = \frac{900 + 300 - 1200}{27} = 0$.
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