A new lottery ticket on the market has players pay $2 to have the chance to win up to $1,000 instantly in cash prizes. Let X be the discrete random variable of cash prizes available. X can take the values of $0, $1, $2, $5, $1000. You are told that expected value of winnings per game is $0.45. Which of the following is the best interpretation of the expected value of the cash prize? O a. In the long run, after playing many lottery tickets, players are expected to win $0.45, on average per game played for $2. b. In the long run, after playing many lottery tickets, players are expected to lose $0.45, on average per game played for $2. O c. In the long run, a player will always make a profit. O d. Each time a player buys a lottery ticket, they can expect to lose $0.45 per game played for $2. O e. Each time a player buys a lottery ticket, they can expect to win $0.45 per game played for $2