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

Options

A. `(400)/(3)` gain
B. `(400)/(3)` loss
C. `(400)/(9)` loss
D. 0

Answer

D

Explanation

Total gain will be `[["win" = (5 or 6)/("Total")= (2)/(6)],["loss" = (1,2,3,4)/("total") = (4)/(6)]]`
`100 xx ["win"] + ["Loss"]["win"][-50+100] + [Loss]["Loss"]["win"][-50-50+100] + ("loss")("loss")("loss")[-50-50-50]`
`= (1)/(3) xx 100 + (2)/(3).(1)/(3).50 + (2)/(3).(2)/(3).(1)/(2)[0] + (2)/(3).(2)/(3).(2)/(3)(-150) = 0`