Say that you go to a casino and decide to play roulette. You've been learning so much from your statistics class that you want to calculate some statistics about the game. To play roulette, a wheel is spun and a ball goes around the wheel until it lands on one of 38 spaces, which have the numbers 0,00 and 1-36. The numbers 0 and 00 are both colored green, while half (18) of the remaining numbers are colored red and the rest are colored black. say that you bet $10 that the ball lands on a red square, and after the first round, you make a second $20 bet that the ball lands on a number from 1-18. If you win a bet you win that amount of money. For example, if you win the first bet you get your $10 back from the bet plus an additional $10 for a net gain of $10.

1. Find each of the following probabilities P(ball lands on red, P(ball lands on 1-18), P(you win both bets), P(you lose both bets). You may assume that half of the numbers between 1-18 are red.

2. Give a probability distribution for the money you win while making your bet.

1. Find the expected value of your earnings and the variance of your winnings.