A probability experiment is conducted in which the sample space of the experiment is S={9,10,11,12 ,13,14,15,16,17,18,19,20}, and event E={9, 10, 11, 12, 13, 14} and event G={16, 17, 18, 19}. Assume that each outcome is equally likely. List the outcomes in E and G. Are E and G mutually​ exclusive?

Given the information, we have:

- The sample space \( S = \{9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\} \).
- Event \( E = \{9, 10, 11, 12, 13, 14\} \).
- Event \( G = \{16, 17, 18, 19\} \).

### List the outcomes in \( E \) and \( G \):
- Outcomes in \( E \): \( \{9, 10, 11, 12, 13, 14\} \).
- Outcomes in \( G \): \( \{16, 17, 18, 19\} \).

### Are \( E \) and \( G \) mutually exclusive?

Two events are **mutually exclusive** if they cannot occur simultaneously, meaning their intersection is empty (no common outcomes between the events).

To check if \( E \) and \( G \) are mutually exclusive, we need to determine the intersection \( E \cap G \).

- \( E \cap G = \{\} \) (there are no common outcomes between the sets \( E \) and \( G \)).

Since \( E \cap G = \emptyset \), **\( E \) and \( G \) are mutually exclusive**.

Would you like further details or have any other questions?

Here are 5 related questions:
1. How do you calculate the probability of mutually exclusive events?
2. What happens to the probability formula if two events are not mutually exclusive?
3. Can events be independent and mutually exclusive at the same time?
4. What is the probability of the union of mutually exclusive events?
5. How do you define the complement of an event in a sample space?

**Tip:** When events are mutually exclusive, the probability of their union is simply the sum of their individual probabilities.

Explore the concept of mutually exclusive events in probability using a specific example. Learn how to determine if events are mutually exclusive and their implications in probability theory. Suitable for Grades 9-12.

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