A lottery is a game that some organizations use to raise money. It works like th

Question

A lottery is a game that some organizations use to raise money. It works like this: each player buys a ticket. All the tickets have distinct numbers. The money raised from selling tickets goes into a bank account. When the lottery is over, the number of a sold ticket is chosen at random. The player whose ticket has that number wins some of the money from the account, called the payoff.
      Suppose there are three lotteries, called A, B, and C. For each lottery, the following table shows how many people play, and the payoff.

LOTTERY

PLAYERS

PAYOFF

A

100

$1.00

B

1000

$100.00

C

10,000

$1000.00

There is a player who will buy one ticket from any of the three lotteries. Based on the expected value of the payoffs, which lottery should the player buy a ticket from?

LOTTERY

PLAYERS

PAYOFF

A

100

$1.00

B

1000

$100.00

C

10,000

$1000.00

Explanation / Answer

Lottery A: Probability of win = 1/100. So, expected payoff = $1 * (1/100) = 1/100

Lottery B: Probability of win = 1/1000. So, expected payoff = $100 * (1/1000) = 1/10

Lottery C: Probability of win = 1/10000. So, expected payoff = $10000 * (1/1000) = 1/10

So, the player can buy from the lottery B or C since bith have the same expected payoffs and is higher than A.

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