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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

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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