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 :

Question

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

Tardigrade Admin · Accepted Answer

Expected Gain/ Loss = = w Ã 100 + Lw (-50 + 100) + L2w (-50 -50 + 100) + L3 (-150) = (1/3) × 100 + (2/3) . (1/3)(50) + ((2/3))2 ((1/3)) (0) + ((2/3))3 (-150) = 0 here w denotes probability that outcome 5 or 64 ( w = (2/6) = (1/3)) here L denotes probability that outcome 1,2,3,4 (L= (4/6) = (2/3))

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 :

$\frac{400}{3}$ gain

$\frac{400}{3}$ loss

$0$

$\frac{400}{9}$ loss

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 :

3400​ gain

3400​ loss

0

9400​ loss

Expected Gain/ Loss = = w × 100 + Lw (-50 + 100) + L2w (-50 -50 + 100) + L3 (-150) =31​×100+32​.31​(50)+(32​)2(31​)(0)+(32​)3(−150)=0 here w denotes probability that outcome 5 or 64 ( w = 62​=31​) here L denotes probability that outcome 1,2,3,4(L=64​=32​)

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 :

$\frac{400}{3}$ gain

$\frac{400}{3}$ loss

$0$

$\frac{400}{9}$ loss