Business Finance Homework Help

The Governor for the State of Alabama is considering starting a weekly lottery to help raise money for the state. The Governor’s buddies have devised a game where participants must pick six numbers from a set of possible winning numbers. The more winning numbers the participant picks correctly, the greater the prize. The cost to participants is $1 for each entry into the game. On the back of each ticket is the following information regarding the probability of winning specific amounts of cash.

Numbers Matched

Prize
x

Probability
P(x)

1

$1

0.4130195

2

$10

0.132378

3

$100

0.0176504

4

$1,000

0.0009686

5

$10,000

0.0000184

6

$100,000

0.0000001

Note the following:

• The $1 fee to play the game is a sunk cost for the contestant. That is, regardless of how many, if any, numbers the contestant matches, the contestant does not get the $1 back. In the case of the contestant matching 2 numbers, the contestant pays $1 to play and wins $10, so the contestant’s net winnings are $9.
• The grand prize is fixed at $100,000, unlike other lotteries where the amount varies each week according to the number of contestants and winners during the previous week.
• Assume the probabilities provided above are accurate.

Your cousin Louie tells you that he is going to buy one ticket every week, and he will have won almost $200 by the end of the year.

1. Should the governor rethink the lottery?
2. Do you have any suggestions for improving the lottery?
3. Is Louie correct about pocketing approximately $200?