# Question: Many state governments use lotteries to raise money for public

Many state governments use lotteries to raise money for public programs. In a common type of lottery, a customer buys a ticket with a three-digit number from 000 to 999. A machine (such as one with bouncing balls numbered 0 to 9) then selects a number in this range at random. Each ticket bought by a customer costs $1, whether the customer wins or loses. Customers with winning tickets are paid $500 for each winning ticket.

(a) Sketch the probability distribution of the random variable X that denotes the net amount won by a customer. (Notice that each customer pays $1 regardless of whether he or she wins or loses.)

(b) Is this a fair game? (See Exercise 31 for the definition of a fair game.) Does the state want a fair game?

(c) Interpret the expected value of X for a person who plays the lottery.

(a) Sketch the probability distribution of the random variable X that denotes the net amount won by a customer. (Notice that each customer pays $1 regardless of whether he or she wins or loses.)

(b) Is this a fair game? (See Exercise 31 for the definition of a fair game.) Does the state want a fair game?

(c) Interpret the expected value of X for a person who plays the lottery.

**View Solution:**## Answer to relevant Questions

Another way to define a fair game is that a playerâ€™s probability of winning must be equal to the playerâ€™s share of the pot of money awarded to the winner. All money is put into a pot at the start of the game, and the ...Imagine that the investor in Exercise 37 invests $10,000 for one month in a company whose stock either goes up by 80% after a month with probability 1>2 or drops 60% with probability 1 > 2. After one month, the investor ...A manufacturer of inexpensive printers offers a model that retails for $150. Each sale of one of these models earns the manufacturer $60 in profits. The manufacturer is considering offering a $30 mail-in rebate. Assume that ...These data are daily percentage changes of several stocks in 2010 and 2011. This question focuses on stock in Apple. (a) Describe the shape and any key features of the histogram of percentage changes in Apple stock. (b) Find ...If an investor decides on the all-Microsoft portfolio (in the text example), does it make sense to use the Sharpe ratio to decide whether to invest $2,000 or $4,000?Post your question