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 :
Correct Option: , 3
Expected Gain/ Loss $=$
$=\mathrm{w} \times 100+\mathrm{Lw}(-50+100)+\mathrm{L}^{2} \mathrm{w}(-50-50+$
$100)+\mathrm{L}^{3}(-150)$
$=\frac{1}{3} \times 100+\frac{2}{3} \cdot \frac{1}{3}(50)+\left(\frac{2}{3}\right)^{2}\left(\frac{1}{3}\right)(0)+$
$\left(\frac{2}{3}\right)^{3}(-150)=0$
here $\mathrm{L}$ denotes probability that outcome
$1,2,3,4\left(\mathrm{~L}=\frac{4}{6}=\frac{2}{3}\right)$
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