1. Analyze the wheel. Why do you think it was designed the way it was?
The wheel was designed so that the player is more likely to land on “no prize” than on a valuable prize. The largest sections are the “no prize” spaces, while the money prizes and jackpot are much smaller. This makes the game exciting for the player and helps the booth owner make a profit.
2. Probability of a favorable result, meaning not landing on “no prize.”
About 40% of the wheel is “no prize.”
So the probability of not landing on “no prize” is:
100% − 40% = 60%
Answer: about 60%, or 0.60.
3. Probability of landing on “small prize” or “medium prize.”
The small prize section is about 14% of the wheel.
The medium prize section is about 14% of the wheel.
14% + 14% = 28%
Answer: about 28%, or 0.28.
4. Probability of winning money with one spin.
The money sections are 5, 10, and jackpot.
The 5 section is about 5%.
The 10 section is about 5%.
The jackpot section is about 2%.
5% + 5% + 2% = 12%
Answer: about 12%, or 0.12.
5. Expected outcome for 60 spins.
Multiply each probability by 60.
No prize: 40% of 60 = 24 times
Small prize: 14% of 60 = about 8 times
Medium prize: 14% of 60 = about 8 times
Large prize: 10% of 60 = 6 times
Re-spin: 10% of 60 = 6 times
5: 5% of 60 = 3 times
10: 5% of 60 = 3 times
Jackpot: 2% of 60 = about 1 time
6. Is the wheel profitable for the booth owner?
The wheel is probably profitable for the booth owner because the largest sections are “no prize.” Out of 60 spins, the wheel would be expected to land on “no prize” about 24 times. It would land on the jackpot only about 1 time. Since the expensive prizes have smaller sections, the booth owner does not have to give away valuable prizes very often.
7. How could the booth owner make the wheel more profitable?
The booth owner could make the “no prize” sections larger and make the jackpot, large prize, and money sections smaller. This would lower the probability of winning valuable prizes. The booth owner could also replace some prize sections with more “re-spin” or “small prize” sections so that players still feel like they have a chance to win, but the booth gives away fewer expensive prizes.
