1) The Dodgers beat the Giants in 53% of the games they play. If the Dodgers and the Giants play three games, what is the probability that the Dodgers will win exactly 2 games?

2) There is a lottery in which you pay $1 and pick 3 digits. A three-digit number is then picked randomly and you get $600 if that number is the one you picked. Otherwise you get nothing. What is the expected amount of your winnings? (Note: winnings is the difference between what you spent and what you got.)

3) Let random variable X represent the grade students obtain at a certain high school in California. The values of X can be 0 (for F), 1 (for D), 2 (for C), 3 (for B), and 4 (for A). The probability of an F is 0.05, of a D is 0.10, of a C is 0.35, of a B is 0.30, and of an A is 0.20. What is the expected value of X?

4) What is the standard deviation of X, using the same random variable X as in the previous problem?

5) Let random variable X represent the number of heads in three flips of a coin that is weighted 0.7 towards heads. In other words, X ~ Binom(3, 0.7). What is the expected value of X?

6) What is the variance of X, using the same random variable X as in the previous problem?