https://file.aiquickdraw.com/mathbot/file/1728935554893xdy9l0dm.jpg

Let's analyze the situations in the image to determine whether they represent **independent** or **not independent** events.

1. **A spinner is divided into three same-sized sections. The spinner is spun three times.**
   - **Answer:** Independent  
     Explanation: The outcome of each spin is independent of the others. The result of one spin doesn't affect the outcome of any subsequent spins.

2. **A number cube (die) is rolled twice.**
   - **Answer:** Independent  
     Explanation: Each roll is independent of the other since the outcome of one roll does not impact the next.

3. **A bag contains 8 white balls and 3 yellow balls. Two balls are selected from the bag without replacement.**
   - **Answer:** Not independent  
     Explanation: Since the balls are drawn **without replacement**, the second draw depends on the outcome of the first draw (the total number of balls changes, and so do the probabilities).

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Do you need further clarification or details?

Here are **five related questions** to expand your understanding:
1. What are examples of dependent events besides drawing without replacement?
2. How does "with replacement" change event independence?
3. How can we calculate the probability of independent events occurring together?
4. What is the formula for conditional probability for dependent events?
5. Can real-world problems contain a mix of independent and dependent events?

**Tip:** For independent events, the probabilities multiply. For dependent events, you need to adjust probabilities as events unfold!

A spinner is divided into three same-sized sections. The spinner is spun three times. A number cube is rolled twice. A bag contains 8 white balls and 3 yellow balls. Two balls are selected from the bag without replacement. Determine if these situations represent independent or not independent events.

Explore how to determine whether events are independent or dependent in probability. This problem covers examples of spinning a spinner, rolling a die, and drawing balls from a bag without replacement. It includes key concepts like the multiplication rule for independent events and conditional probability.

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