Question

In a card game Reena wins 3 Rs. if she draws a king or a spade and 7 Rs. if a heart or a queen from an pack of 52 playing cards. If she pays a certain amount of money each time she will lose the game. What will be the amount so that the game will come out a fair game?

(a) 15

(b) 6

(c) 23

(d) 2

The question was posed to me in homework.

I'd like to ask this question from Discrete Probability topic in section Discrete Probability of Discrete Mathematics

Answer 1

The correct choice is (d) 2

For explanation: We know that E(X) = ∑{xi * P(xi)} = 3 * \(\frac{2}{13} + 7 * \frac{2}{13} − x * \frac{10}{13} = \frac{20}{13} − \frac{10x}{13}\). Suppose the expected value should be 0 Rs. for the game to be fair. So \(\frac{20}{13} − \frac{10x}{13}\) = 0 ⇒ x=2. So she should pay Rs.2 for it to be a fair game.