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  4. In a game, a man wins Rs. 100 if he gets 5 of 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 :

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Q. In a game, a man wins Rs. $100$ if he gets $5$ of $6$ 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 :

JEE MainJEE Main 2019Probability - Part 2

Solution:

Expected Gain/ Loss =
= w × 100 + Lw (-50 + 100) + L$^2$w (-50 -50 + 100) + L$^3$ (-150)
$= \frac{1}{3} \times 100 + \frac{2}{3} . \frac{1}{3}(50) \, + \bigg(\frac{2}{3}\bigg)^2 \, \bigg(\frac{1}{3}\bigg) (0) + \bigg(\frac{2}{3}\bigg)^3 (-150) = 0$
here w denotes probability that outcome $5$ or $64$ (
$w$ = $\frac{2}{6} \, = \, \frac{1}{3})$
here L denotes probability that outcome
$1,2,3,4 (L= \frac{4}{6} = \frac{2}{3})$