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Let's break down the problem in the image, starting with the table and questions.

### Table Summary:
The table provides the number of marbles based on color and material (Glass, Steel, Plastic). There are 324 total marbles. Here's the breakdown:

|               | Glass | Steel | Plastic | Total |
|---------------|-------|-------|---------|-------|
| **Red**       | 9     | 66    | 34      | 109   |
| **Green**     | 8     | 42    | 13      | 63    |
| **Blue**      | 91    | 14    | 47      | 152   |
| **Total**     | 108   | 122   | 94      | 324   |

### Questions and Solutions:

#### a) What is the probability that marble is Green and made of Steel?
The number of Green marbles made of Steel is 42, and the total number of marbles is 324.

\[
P(\text{Green and Steel}) = \frac{42}{324} = \frac{7}{54}
\]

#### b) What is the probability that marble is Green?
The total number of Green marbles is 63, and the total number of marbles is 324.

\[
P(\text{Green}) = \frac{63}{324} = \frac{7}{36}
\]

#### c) What is the probability that marble is made of Steel?
The total number of Steel marbles is 122, and the total number of marbles is 324.

\[
P(\text{Steel}) = \frac{122}{324} = \frac{61}{162}
\]

#### d) What is the probability that marble is Green given that it is made of Steel?
This is a conditional probability. The number of Green marbles made of Steel is 42, and the total number of Steel marbles is 122.

\[
P(\text{Green | Steel}) = \frac{42}{122} = \frac{21}{61}
\]

#### e) What is the probability that marble is made of Steel given that it is Green?
This is another conditional probability. The number of Green marbles made of Steel is 42, and the total number of Green marbles is 63.

\[
P(\text{Steel | Green}) = \frac{42}{63} = \frac{2}{3}
\]

#### f) What is the probability that marble is Blue given that it is made of Steel?
The number of Blue marbles made of Steel is 14, and the total number of Steel marbles is 122.

\[
P(\text{Blue | Steel}) = \frac{14}{122} = \frac{7}{61}
\]

#### g) What is the probability that marble is made of Steel given that it is Blue?
The number of Blue marbles made of Steel is 14, and the total number of Blue marbles is 152.

\[
P(\text{Steel | Blue}) = \frac{14}{152} = \frac{7}{76}
\]

Would you like any further details on these solutions?

### Related Questions:
1. What is the probability that a marble is Red and made of Plastic?
2. What is the probability that a marble is Blue and made of Glass?
3. What is the probability that a marble is Red given that it is made of Steel?
4. What is the probability that a marble is Plastic given that it is Green?
5. What is the probability that a marble is made of Glass given that it is Blue?

#### Tip:
When calculating conditional probabilities, always focus on narrowing the denominator to the specific condition in question.

What is the probability of different outcomes based on the color and material of marbles in a jar, such as finding the probability of a marble being Green and made of Steel?

Learn how to calculate probabilities for marble outcomes, such as the probability of selecting a marble that is Green and made of Steel, or the conditional probability of a marble being Green given that it is made of Steel. This exercise involves key probability concepts and conditional probability theorems. Suitable for Grades 9-12.

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