**Problem 7.** Consider the following table formed by a population of 70.\[\begin{array}{c|c|c} & A & B \\\hlineX & 22 & 17 \\Y & 18 & 13 \\\end{array}\]**Part A.** Find $ P(A) $, $ P(B) $, $ P(X) $, $ P(Y) $.**Part B.** Find the probability of $ X \cap B $ and $ X \cup B $.**Part C.** Find the conditional probability of $ P(X|A) $ and $ P(B|Y) $.---### Explanation of the Table:The table represents a population divided into different categories. The rows are labeled as $ X $ and $ Y $, and the columns are labeled as $ A $ and $ B $. The numbers in the table represent the count of individuals in each category.- The number 22 corresponds to category $ X $ and column $ A $.- The number 17 corresponds to category $ X $ and column $ B $.- The number 18 corresponds to category $ Y $ and column $ A $.- The number 13 corresponds to category $ Y $ and column $ B $.The total population is given as 70.

Name: **Problem 7.** Consider the following table formed by a population of
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Description: **Problem 7.** Consider the following table formed by a population of 70.\[\begin{array}{c|c|c} & A & B \\\hlineX & 22 & 17 \\Y & 18 & 13 \\\end{array}\]**Part A.** Find $ P(A) $, $ P(B) $, $ P(X) $, $ P(Y) $.**Part B.** Find the probability

A B Total X 22 17 39 Y 18 13 31 Total 40 30 70

Math

Statistics

Problem 7. Consider the following table formed by a population of 70. AB X 22 17 Y 18 13 Part A. Find P(A), P(B), P(X), P(Y). Part B. Find the probability of X n B and XU B. Part C. Find the conditional probability of P(X|A) and P(B|Y).

Problem 7. Consider the following table formed by a population of 70. AB X 22 17 Y 18 13 Part A. Find P(A), P(B), P(X), P(Y). Part B. Find the probability of X n B and XU B. Part C. Find the conditional probability of P(X|A) and P(B|Y).

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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Question

**Problem 7.** Consider the following table formed by a population of 70.

\[
\begin{array}{c|c|c}
& A & B \\
\hline
X & 22 & 17 \\
Y & 18 & 13 \\
\end{array}
\]

**Part A.** Find $ P(A) $, $ P(B) $, $ P(X) $, $ P(Y) $.

**Part B.** Find the probability of $ X \cap B $ and $ X \cup B $.

**Part C.** Find the conditional probability of $ P(X|A) $ and $ P(B|Y) $.

---

### Explanation of the Table:

The table represents a population divided into different categories. The rows are labeled as $ X $ and $ Y $, and the columns are labeled as $ A $ and $ B $. The numbers in the table represent the count of individuals in each category.

- The number 22 corresponds to category $ X $ and column $ A $.
- The number 17 corresponds to category $ X $ and column $ B $.
- The number 18 corresponds to category $ Y $ and column $ A $.
- The number 13 corresponds to category $ Y $ and column $ B $.

The total population is given as 70.

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