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The problem asks to calculate various probabilities based on the number of marbles of different colors. Here's the breakdown of the information:

- 20 red marbles
- 23 green marbles
- 22 blue marbles
- Total marbles: \( 20 + 23 + 22 = 65 \)

Let's solve each part:

1. **Probability of drawing a red marble**:  
   \( P(\text{red}) = \frac{\text{Number of red marbles}}{\text{Total marbles}} = \frac{20}{65} \)

2. **Probability of drawing a green marble**:  
   \( P(\text{green}) = \frac{\text{Number of green marbles}}{\text{Total marbles}} = \frac{23}{65} \)

3. **Probability of drawing a blue marble**:  
   \( P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total marbles}} = \frac{22}{65} \)

4. **Probability of drawing a marble that is not blue**:  
   Marbles that are not blue = Red marbles + Green marbles = \( 20 + 23 = 43 \)  
   \( P(\text{not blue}) = \frac{43}{65} \)

5. **Probability of drawing a marble that is both red and blue**:  
   It is not possible to have a marble that is both red and blue, so the probability is:  
   \( P(\text{red and blue}) = 0 \)

6. **Probability of drawing a marble that is either red or blue**:  
   Red marbles + Blue marbles = \( 20 + 22 = 42 \)  
   \( P(\text{red or blue}) = \frac{42}{65} \)

Would you like more details or have any questions on these steps?

Here are 5 related questions:
1. How do we calculate the probability of two independent events happening together?
2. How can we determine the probability of a complement event, such as "not blue"?
3. What is the principle behind mutually exclusive events in probability?
4. How would the total probability change if more marbles of a new color were added?
5. How does the concept of conditional probability apply if we knew the marble was not blue?

**Tip**: Always ensure the total probability of all outcomes in a sample space sums to 1!

A marble is drawn randomly from a jar with 20 red marbles, 23 green marbles, and 22 blue marbles. The problem asks for the probability of drawing: a red marble, a green marble, a blue marble, a marble that is not blue, a marble that is both red and blue, and a marble that is either red or blue.

Solve a probability problem involving a jar with 20 red marbles, 23 green marbles, and 22 blue marbles. Learn how to calculate the probability of drawing a red marble, a green marble, a blue marble, and more. This problem covers key concepts like complementary events and mutually exclusive events.

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