What if the manufacturer guarantees 4 winning bottles in every 24 bottles?

If a manufacturer guarantees 4 winning bottles in every 24 bottles, this implies that there is a **probability** associated with picking a winning bottle from the set. This setup is useful for modeling scenarios like promotions or probability experiments. Here's a breakdown:

### Key Information:
- **Total bottles**: 24
- **Winning bottles**: 4
- **Non-winning bottles**: 24 - 4 = 20

### Probability of Selecting a Winning Bottle:
The probability \( P \) of picking a winning bottle from the 24 bottles is:
\[
P(\text{winning}) = \frac{\text{Number of winning bottles}}{\text{Total number of bottles}} = \frac{4}{24} = \frac{1}{6}
\]
Thus, the probability of picking a winning bottle at random is \( \frac{1}{6} \).

### Probability of Selecting a Non-Winning Bottle:
The probability \( P \) of picking a non-winning bottle is:
\[
P(\text{non-winning}) = \frac{\text{Number of non-winning bottles}}{\text{Total number of bottles}} = \frac{20}{24} = \frac{5}{6}
\]

### Interpretation:
- If you pick a bottle at random from the 24 bottles, you have a \( \frac{1}{6} \) chance of selecting a winning bottle and a \( \frac{5}{6} \) chance of selecting a non-winning bottle.
- This could apply in various contexts, such as promotions where every 6th bottle (on average) might be a winner.

Would you like further details or explanations on probability applications, combinations, or related scenarios?

Here are 5 related questions:
1. What is the probability of picking two winning bottles in a row without replacement?
2. How can this scenario be modeled using a binomial distribution?
3. What is the expected number of winning bottles in a set of 24?
4. How does the probability change if you increase the number of bottles to 48 but maintain the same winning ratio?
5. How would the odds change if the number of winning bottles was increased to 6 in every 24?

**Tip**: When calculating probabilities, be sure to differentiate between sampling **with** and **without replacement**.

Learn how to calculate the probability of selecting a winning bottle when a manufacturer guarantees 4 winning bottles in every 24. This problem involves basic probability concepts, fractions, and sampling methods. Suitable for students in Grades 6-8.

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