### JEE Main 12 Jan 2019 Evening Question 5

##### Question: 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]

#### Options:

A) $ \frac{400}{9}loss $

B) $ \frac{400}{3}gain $

C) 0

D) $ \frac{400}{3}loss $

## Show Answer

#### Answer:

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)+{{( \frac{2}{3} )}^{3}}(-150) $ $ =\frac{100}{3}+\frac{100}{9}-\frac{8}{27}\times 150=0 $