A game involves you choosing one number (between 1 to 6 inclusive) and then throwing three fair dice simultaneously. If none of the dice shows up the number that you have chosen, you lose Rs. 1. If exactly one, two or three dice show up the number that you have chosen, you win Rs. 1, Rs. 3 or Rs. 5 respectively. What is your expected gain?
Please suggest some other questions of this kind, if you have any.