Question
Determine whether the second scenario would be dependent or independent of the first scenario. Explain.
Pulling a marble out of a bag, then pulling a marble out of the same bag.
Question 1 options:
There is not enough information to determine a relationship.
Dependent
Independent
Pulling a marble out of a bag, then pulling a marble out of the same bag.
Question 1 options:
There is not enough information to determine a relationship.
Dependent
Independent
Answers
GPT-4o mini
In the given scenarios of pulling a marble out of a bag, then pulling a marble out of the same bag, the second scenario is **dependent** on the first scenario.
### Explanation:
1. **Dependent Events**: In probability, two events are dependent if the outcome or occurrence of the first event affects the outcome or occurrence of the second event.
2. **Scenario Analysis**:
- When you pull the first marble out of the bag, the total number of marbles remains unchanged until you remove the marble.
- When you pull the second marble from the same bag, the total number of marbles has decreased by 1 (since one marble has already been removed).
- Therefore, the probability of drawing a specific marble on the second draw is influenced by what happened in the first draw.
3. **Conclusion**: Since the second pull relies on the first pull and the composition of the remaining marbles in the bag changes, these two events are dependent.
Thus, the correct option is **Dependent**.
### Explanation:
1. **Dependent Events**: In probability, two events are dependent if the outcome or occurrence of the first event affects the outcome or occurrence of the second event.
2. **Scenario Analysis**:
- When you pull the first marble out of the bag, the total number of marbles remains unchanged until you remove the marble.
- When you pull the second marble from the same bag, the total number of marbles has decreased by 1 (since one marble has already been removed).
- Therefore, the probability of drawing a specific marble on the second draw is influenced by what happened in the first draw.
3. **Conclusion**: Since the second pull relies on the first pull and the composition of the remaining marbles in the bag changes, these two events are dependent.
Thus, the correct option is **Dependent**.