A jar contains 4 red marbles numbered 1 to 4 and 12 blue marbles numbered 1 to 12. A marble is drawn at random from the jar. Round your answer to four decimal places. Find the probability that the
marble is red:

marble is odd-numbered:

marble is red or blue:

Let's solve each probability step by step.

### Total Number of Marbles
- There are 4 red marbles and 12 blue marbles, so the total number of marbles is:
\[
4 + 12 = 16
\]

---

### 1. **Probability that the marble is red**:
- There are 4 red marbles out of a total of 16 marbles. Therefore, the probability is:
\[
P(\text{Red}) = \frac{4}{16} = 0.25
\]

---

### 2. **Probability that the marble is odd-numbered**:
- Red odd-numbered marbles: 1, 3 (2 red marbles).
- Blue odd-numbered marbles: 1, 3, 5, 7, 9, 11 (6 blue marbles).

So, there are a total of \(2 + 6 = 8\) odd-numbered marbles out of 16 marbles. Therefore, the probability is:
\[
P(\text{Odd}) = \frac{8}{16} = 0.5
\]

---

### 3. **Probability that the marble is red or blue**:
- Every marble in the jar is either red or blue, so the probability that a marble is red or blue is:
\[
P(\text{Red or Blue}) = \frac{16}{16} = 1
\]

---

### Final Answer (Rounded to Four Decimal Places):
- Probability that the marble is red: **0.2500**
- Probability that the marble is odd-numbered: **0.5000**
- Probability that the marble is red or blue: **1.0000**

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Do you want more details on any step, or have any questions?

Here are 5 related questions to explore further:

1. What is the probability that the marble is blue?
2. What is the probability that the marble is even-numbered?
3. What is the probability that the marble is both red and odd-numbered?
4. What is the probability that the marble is blue and even-numbered?
5. What is the probability of drawing a specific marble, such as the red marble numbered 2?

**Tip**: In probability, "or" events combine different categories, so remember that overlapping categories need to be handled carefully to avoid double-counting.

A jar contains 4 red marbles numbered 1 to 4 and 12 blue marbles numbered 1 to 12. A marble is drawn at random from the jar. Round your answer to four decimal places. Find the probability that the marble is red, the marble is odd-numbered, and the marble is red or blue.

This problem explores the probability of drawing a red marble, an odd-numbered marble, or any marble (red or blue) from a jar containing 4 red and 12 blue marbles. Detailed calculations include favorable outcomes for each scenario and the application of basic probability formulas. Suitable for students in Grades 6-8.

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