Answer These Questions

Question

WHEEL https://pastebin.com/cj121kWX

1. Analyze the wheel. Why do you think it was designed the way it was? Use complete sentences

2. If a person spins the wheel once, what is the probability that the results will end favorably (they do not land on 0)? Show your work and explain your process.

3. What is the probability that a player will land on "small prize" or "medium prize" with one spin? Show your work and explain your process.

4. What is the probability that a player will win money with one spin? Show your work and explain your process.

5. Joey decides to spin the wheel 60 times. What is the expected outcome of spins? (How many times should it land on each space?)

6. Use your information from question 5 to determine whether or not this wheel is profitable for the person who owns the booth. Explain your reasoning in full sentences.

7. What could the booth owner do to make the wheel more profitable for himself? You may include a drawing of the more profitable wheel if you would like. Explain your reasoning in complete sentences.

Answer 1

1. The wheel was designed to maximize profit for the owner while still enticing players to play. The "No Prize" sections are the largest individual sections on the wheel, visually taking up 50% of the total area, which ensures that the "house" wins most of the time. Conversely, the most desirable outcome, the "JACKPOT," is the smallest sliver, making it statistically very unlikely to hit.
2. The probability is 1/2 or 50 percent. Visually, the two black "no prize" wedges are 90-degree angles each. If you combine them, they take up exactly half of the circle. This means the chance of landing on a winning spot is the remaining half.
3. The probability is 1/4 or 25 percent. The "small prize" and "medium prize" sections sit next to each other and occupy the entire bottom quarter of the wheel. Since they take up one quarter of the circle, the probability is 1 out of 4.
4. he probability is approximately 1/12 or about 8.3 percent. The sections labeled with money (5, 10, and Jackpot) are located in the top quarter of the wheel. Visually, these thin slices take up about one-third of that specific quarter. One-third of one-quarter results in a probability of 1/12.
5. Based on the probabilities, the expected outcome for 60 spins is:

No Prize: 30 times (half the spins).

Small Prize: about 7 or 8 times.

Medium Prize: about 7 or 8 times.

Re-spin: about 5 times.

Large Prize: about 5 times.

Money Wins (5, 10, Jackpot): about 5 times combined.

1. Yes, this wheel is profitable for the owner. Because the wheel lands on "no prize" 30 out of 60 times, the owner collects money for those spins without giving anything away. Additionally, the most common prizes (small and medium) are usually cheap items. The expensive payouts, like the Jackpot or cash, happen very rarely, so the entry fees from the losing spins will easily cover the cost of the prizes.
2. To make the wheel more profitable, the owner could increase the size of the black "no prize" sections so they take up more than half the wheel. He could also remove the "re-spin" section, which currently gives players a free second chance to win, and replace it with another losing section or a very small prize.