A die is thrown. You win as many rupees as the number on the die if it is even, and lose ₹2 if it is odd. What is your expected gain per throw?

Explanation

1. 01

   Gains: ₹2, ₹4, ₹6 each with probability $\frac{1}{6}$, and $-2$ with probability $\frac{1}{2}$.

2. 02

   $E = \frac{2 + 4 + 6}{6} - 2 \times \frac{1}{2} = 2 - 1 = 1$ rupee.