A jar contains 3 red marbles numbered 1 to 3 and 4 blue marbles numbered 1 to 4. A marble is drawn at random from the jar. Find the probability that the marble is red or even-numbered.

To solve this problem, we need to find the probability that the marble drawn is either red or even-numbered.

### Step 1: Determine the total number of marbles
The jar contains:
- 3 red marbles: \( R_1, R_2, R_3 \)
- 4 blue marbles: \( B_1, B_2, B_3, B_4 \)

So, the total number of marbles is:
\[
3 \text{ (red)} + 4 \text{ (blue)} = 7 \text{ (total marbles)}
\]

### Step 2: Identify the favorable outcomes (red or even-numbered)
We are looking for marbles that are either red or even-numbered. Let's break this down:
- **Red marbles**: \( R_1, R_2, R_3 \) (3 outcomes)
- **Even-numbered marbles**: \( R_2, B_2, B_4 \) (3 outcomes)

Note that \( R_2 \) is both red and even, so we need to be careful not to count it twice. The distinct favorable outcomes are:
\[
R_1, R_2, R_3, B_2, B_4
\]
These are 5 favorable outcomes in total.

### Step 3: Calculate the probability
The probability is the ratio of favorable outcomes to the total number of outcomes:
\[
P(\text{red or even}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{5}{7}
\]

Thus, the probability that the marble drawn is either red or even-numbered is \( \frac{5}{7} \).

Would you like more details, or do you have any questions?

### Related Questions:
1. What is the probability of drawing a red marble only?
2. What is the probability of drawing an even-numbered marble only?
3. If two marbles are drawn without replacement, what is the probability both are blue?
4. How does the probability change if the jar contains 5 blue marbles instead?
5. What is the probability of drawing a marble that is both red and odd-numbered?

### Tip:
When dealing with probabilities involving "or," always check for overlap between the two events to avoid double-counting.

Find the probability of drawing a red or even-numbered marble from a jar containing 3 red marbles and 4 blue marbles. Explore key probability concepts and learn how to avoid double-counting outcomes. Suitable for students in Grades 6-8.

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