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 E={12,13,14,15,16,17,18,19}. Assume each outcome is equally likely. List the outcomes in Ec. Find (PEc).

Given the problem:

- The sample space \( S = \{9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\} \)
- The event \( E = \{12, 13, 14, 15, 16, 17, 18, 19\} \)
- Each outcome is equally likely.

### Step 1: Find \( E^c \)
The complement of event \( E \), denoted by \( E^c \), includes all the outcomes in the sample space \( S \) that are not in \( E \).

- \( E^c = S - E \)
- \( E^c = \{9, 10, 11, 20\} \)

### Step 2: Find \( P(E^c) \)
Since each outcome is equally likely, the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.

- Number of outcomes in \( S \) (total outcomes): \( |S| = 12 \)
- Number of outcomes in \( E^c \): \( |E^c| = 4 \)

The probability \( P(E^c) \) is calculated as:

\[
P(E^c) = \frac{|E^c|}{|S|}
\]

\[
P(E^c) = \frac{4}{12} = \frac{1}{3}
\]

### Final Answer:
- The outcomes in \( E^c \) are \( \{9, 10, 11, 20\} \).
- The probability \( P(E^c) = \frac{1}{3} \).

Would you like more details or have any questions? Here are some related questions to consider:

1. How do you calculate the probability of a union of two events?
2. What is the probability of event \( E \) itself?
3. How does the concept of complementary events help in probability?
4. How does the size of the sample space affect the probability of an event?
5. What happens to probabilities if outcomes are not equally likely?

**Tip:** When dealing with probability, always ensure that the sum of the probabilities of all possible outcomes equals 1.

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}. E={12,13,14,15,16,17,18,19}. Assume each outcome is equally likely. List the outcomes in Ec. Find (PEc).

Discover how to find the outcomes and probability of the complementary event Ec in a probability experiment with sample space S={9,10,...,20} and event E={12,13,...,19}. This solution involves key concepts in probability and the Complement Rule. Suitable for Grades 9-10 students.

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