Lottery Expected Value

A student group sells 500 raffle tickets for $2 each. At the drawing the top prize will be a gift certificate for $100. Second prize will be a $50 gift card and there will be five 3rd prizes, each a $20 gift card. What is the expected value of a ticket?

• lose an average of $5.50
• lose an average of $1.50
• win an average of $2.00
• lose an average of $10.00

Suppose you buy a ticket for $6 out of a lottery of 1000 tickets where the prize for the one winning is to be $800. What are your expected winnings (on average)?

• $800 
• -$6.50
• -$6
• -$5.20

Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6

• 14
• 4.67
• 5
• 7.5

One option in the game of roulette is to bet $6 on red. (There are 18 red compartments, 18 black compartments and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $6 you paid to play and you are awarded an additional $6. If the ball does not land on red, you win nothing and you lose your $6 bet. Find the expected payback (on average) for this game if you bet on red.

• -$5.54
• -$0.32
• -$4.48

Name a situation in real life that you could use expected value on.

• carnival games
• sports
• placing bets
• all of the above

Is your expected value always going to be what happens in real life?

• yes
• no

What do you need to determine before you can calculate expected value?

• number of people playing
• probability of winning 
• name of game
• names of people playing

Once you have probability, what else do you need to know to calculate expected value?

• cost of prize
• type of prize

If the expected value is negative, are you expected to win?

• yes
• no

If the expected value is positive, are you expected to win?

• yes
• no