Question

A player rolls a die and receives the same number of rupees as the number of dots on the face that turns up. What should the player pay for each roll if he wants to make a profit of one rupee per throw of the die in the long run?

• A. Rs. 2.50
• B. Rs. 2
• C. Rs. 3.50
• D. Rs. 4

Hint:

Expected value of a fair die is 3.5. Use this as the basis for average payout in such problems.

Answer 1

The Correct Option is C

Step 1: Expected value of a dice roll Each face 1 to 6 is equally likely with probability $\frac{1}{6}$ \[ E = \frac{1+2+3+4+5+6}{6} = \frac{21}{6} = 3.5 \] So average payout = Rs. 3.50 Step 2: Player wants to make Rs. 1 profit Let the amount the player charges per roll = Rs. $x$ To make Rs. 1 profit: \[ x - 3.5 = 1 \Rightarrow x = \boxed{4.5} \] But question asks: what should the player pay if he wants to make Rs. 1 profit? So if he receives Rs. 4.5 and pays Rs. 3.5 → profit = Rs. 1 To get Rs. 1 profit, cost (i.e. pay out) must be Rs. 3.5 \[ \boxed{3.5} \]