Question
Which events are independent? Select three options. Roll a number cube, and then roll the same number cube again. Flip a coin, and then flip the coin a second time. Rraw a card from a deck, replace it, and then draw a second card. Take a marble out of a bag, and then take a second marble out of the bag.
Ask by Knight Nunez. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The independent events are:
1. Rolling a number cube twice.
2. Flipping a coin twice.
3. Drawing a card with replacement and then drawing another card.
Solution
The following three events are **independent**:
1. **Roll a number cube, and then roll the same number cube again.**
- **Explanation:** Each roll of the number cube (die) is independent of the previous roll. The outcome of the first roll does not influence the outcome of the second roll.
2. **Flip a coin, and then flip the coin a second time.**
- **Explanation:** Each coin flip is independent of the previous flip. The result of the first flip doesn't affect the result of the second flip.
3. **Draw a card from a deck, replace it, and then draw a second card.**
- **Explanation:** Replacing the card after the first draw ensures that the second draw is independent of the first. The probabilities remain unchanged because the deck's composition is the same for both draws.
**Note:**
- *Taking a marble out of a bag and then taking a second marble without replacement is **not** independent,* as the first draw affects the probabilities of the second draw.
### Summary of Independent Events:
1. Rolling a number cube twice.
2. Flipping a coin twice.
3. Drawing a card with replacement and then drawing another card.
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Simplify this solution Bonus Knowledge
Rolling a number cube twice is a great example of independent events! The outcome of the first roll doesn't influence the second roll at all—so whether you rolled a 1 or a 6, the odds remain the same for the next roll. It’s like taking two separate spins on a carnival ride, each with its own chance of turning out wild! Flipping a coin twice also showcases independence beautifully. The result of the first flip, whether it's heads or tails, doesn’t change the probability of the outcome on the second flip. It's like flipping a coin for pizza toppings—your choice of pepperoni or pineapple on the first toss won’t affect what pops up on the next!
