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The image contains a probability worksheet related to marbles categorized by material and color. Here's how to interpret the information and solve the problems.

### Table Breakdown:
There are 3 types of marbles (Glass, Steel, and Plastic) and 3 colors (Green, Red, Blue). The totals are also listed:
- **Green:** 15 glass, 3 steel, 0 plastic, total 18.
- **Red:** 13 glass, 10 steel, 3 plastic, total 26.
- **Blue:** 1 glass, 11 steel, 12 plastic, total 24.
- **Grand total of marbles:** 81.

### Question 1:
1. **Determine P(glass):**
   To calculate the probability of selecting a glass marble, divide the total number of glass marbles by the total number of marbles.

   Total glass marbles = 15 (green) + 13 (red) + 1 (blue) = 29.
   Total marbles = 81.

   \[
   P(\text{glass}) = \frac{29}{81}
   \]

2. **Find P(glass | green):**
   This is the conditional probability of selecting a glass marble given that it is green. The formula is:

   \[
   P(\text{glass | green}) = \frac{P(\text{glass and green})}{P(\text{green})}
   \]

   \( P(\text{glass and green}) = \frac{15}{81} \) (since there are 15 green glass marbles out of 81 total marbles).

   \( P(\text{green}) = \frac{18}{81} \) (since there are 18 green marbles out of 81).

   \[
   P(\text{glass | green}) = \frac{\frac{15}{81}}{\frac{18}{81}} = \frac{15}{18} = \frac{5}{6}
   \]

### Question 2:
1. **Determine P(red):**
   Total red marbles = 26.

   \[
   P(\text{red}) = \frac{26}{81}
   \]

2. **Find P(red | steel):**
   Conditional probability of selecting a red marble given that it is steel. We calculate:

   \( P(\text{red and steel}) = \frac{10}{81} \) (since there are 10 red steel marbles).

   Total steel marbles = 3 (green) + 10 (red) + 11 (blue) = 24.

   \[
   P(\text{red | steel}) = \frac{\frac{10}{81}}{\frac{24}{81}} = \frac{10}{24} = \frac{5}{12}
   \]

Let me know if you would like to go over additional details or need help with the next questions!

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### Related Questions:
1. How would you calculate P(plastic)?
2. What is the probability of drawing a blue marble?
3. How do you determine P(steel | blue)?
4. What is the complement of P(glass)?
5. How does the condition of the marble type affect the overall probability?

### Tip:
When solving probability problems, always ensure the condition you're calculating for (like "given" conditions) is properly set up as the denominator.

Determine the probability of selecting different types and colors of marbles from a table of glass, steel, and plastic marbles.

Learn how to calculate the probability of selecting glass, steel, and plastic marbles of different colors. This worksheet covers key concepts in probability and conditional probability, including step-by-step solutions. Suitable for students in Grades 9-12.

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