Can you help me solve this probability complement equation? **Probability Experiment Sample Space Example**In this exercise, a probability experiment is conducted where the sample space $ S $ is defined as $ \{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\} $. We are given the event $ A = \{8, 9, 10, 11, 12\} $. Assuming each outcome is equally likely, we are asked to find the outcomes in $ A^C $ (the complement of $ A $) and compute $ P(A^C) $.**Problem Statement:**Given:- Sample Space, $ S = \{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\} $- Event, $ A = \{8, 9, 10, 11, 12\} $Determine:1. The outcomes in $ A^C $.1. Compute $ P(A^C) $.**Solution:**1. Identify the outcomes in $ A^C $: - $ A^C $ includes all elements in $ S $ that are not in $ A $. - Outcomes in $ A^C = S \setminus A = \{5, 6, 7, 13, 14, 15\} $.2. Compute $ P(A^C) $: - Number of elements in $ S $: $ |S| = 11 $ - Number of elements in $ A^C = 6 $. - Since each outcome is equally likely, $ P(A^C) = \frac{\text{Number of elements in } A^C}{\text{Total number of elements in } S} = \frac{6}{11} $.The answer and explanation given in the multiple-choice question is:- **Option C**: The outcomes in $ A^C $ are $\{5, 6, 7, 13, 14, 15\}$ and $ P(A^C) = \frac{6}{11} $.

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Can you help me solve this probability complement equation?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Contingency Table

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Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Can you help me solve this probability complement equation?

**Probability Experiment Sample Space Example**

In this exercise, a probability experiment is conducted where the sample space $ S $ is defined as $ \{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\} $. We are given the event $ A = \{8, 9, 10, 11, 12\} $. Assuming each outcome is equally likely, we are asked to find the outcomes in $ A^C $ (the complement of $ A $) and compute $ P(A^C) $.

**Problem Statement:**
Given:
- Sample Space, $ S = \{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\} $
- Event, $ A = \{8, 9, 10, 11, 12\} $

Determine:
1. The outcomes in $ A^C $.
1. Compute $ P(A^C) $.

**Solution:**

1. Identify the outcomes in $ A^C $:
- $ A^C $ includes all elements in $ S $ that are not in $ A $.
- Outcomes in $ A^C = S \setminus A = \{5, 6, 7, 13, 14, 15\} $.

2. Compute $ P(A^C) $:
- Number of elements in $ S $: $ |S| = 11 $
- Number of elements in $ A^C = 6 $.
- Since each outcome is equally likely, $ P(A^C) = \frac{\text{Number of elements in } A^C}{\text{Total number of elements in } S} = \frac{6}{11} $.

The answer and explanation given in the multiple-choice question is:
- **Option C**: The outcomes in $ A^C $ are $\{5, 6, 7, 13, 14, 15\}$ and $ P(A^C) = \frac{6}{11} $.

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