1.. (2+4 points) Casinos are a good business to exploit behavioral biases, probability weighting being the most important bias. But let's think about another: Have you ever played the game of roulette? In roulette, a tiny ball gets spun on a wheel which has spokes numbered 0-36 in each bet. Before the draw, you place your bets on one particular number (you can do other bets but let us ignore them for now). If the ball lands on your number when it stops spinning, you win (about 36 dollars for every dollar you bet). Please write down short explanations for the following sub questions.

a) Most people think this game is fair, meaning its expected value of the bet is 0. Can you see why it is not?

b) By the side of every roulette table, there is an electronic board which shows you on which number the ball landed in the previous 10 spins. I get tempted to look at this board before placing my bet every time I play roulette. Is this rational?

Note that the game is necessarily fair, and I know this in each draw, the probability of the ball landing on each spoke is equal.