In the "new and improved" roulette game discussed in question 1 , you play the game and get a green 10 times in a row. Which of the following statements is correct? (Assume that you have neither improved nor gotten worse in skill in this game since you started playing.) The probability of getting a green on your next spin is less than the probability of getting a green on your first spin. The probability of getting a green on your next spin is greater than the probability of getting a green on your first spin. The probability of getting a green on your next spin is equal to the probability of getting a green on your first spin.

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UpStudy AI · Accepted Answer

To solve this problem, we need to understand the concept of independent events in probability, particularly in the context of a game like roulette.

1. **Known Conditions:**
   - You have played the roulette game and got a green result 10 times in a row.
   - The skill level has not changed since you started playing.

2. **Understanding Roulette:**
   - In a standard roulette game, the outcome of each spin is independent of previous spins. This means that the result of one spin does not affect the result of another spin.
   - The probability of landing on green (or any specific outcome) remains constant for each spin, regardless of previous results.

3. **Analyzing the Statements:**
   - **Statement 1:** The probability of getting a green on your next spin is less than the probability of getting a green on your first spin.
     - This is incorrect because the probability does not change based on previous outcomes.
   
   - **Statement 2:** The probability of getting a green on your next spin is greater than the probability of getting a green on your first spin.
     - This is also incorrect for the same reason; the probability remains constant.
   
   - **Statement 3:** The probability of getting a green on your next spin is equal to the probability of getting a green on your first spin.
     - This is correct because the outcome of each spin is independent, and the probability remains the same.

4. **Conclusion:**
   - The correct statement is: **The probability of getting a green on your next spin is equal to the probability of getting a green on your first spin.**

This conclusion is based on the principle of independence in probability, which states that past events do not influence future events in scenarios like roulette.
The probability of getting a green on your next spin is the same as on your first spin.

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