Round all probabilities to the nearest thousand ### High School Standardized Test Analysis#### Exercise: Assessing Independence of EventsA group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.#### Table of Test Results:| | Passed | Failed ||-----------|--------|--------|| **Male** | 81 | 84 || **Female**| 70 | 5 |#### Problem Statement:Since P(male) × P(pass) = [______] and P(male and pass) = [______], the two results are [______] so the events are [______].#### Explanation of the Table:- The table displays the number of male and female students who passed and failed the test. - **Male:** 81 passed, 84 failed - **Female:** 70 passed, 5 failedThe task involves calculating the probabilities to determine if the events "being male" and "passing the test" are independent.#### Instructions for Completion:1. Calculate \( P(male) \): \( P(male) = \frac{\text{Number of males}}{\text{Total number of students}} \)2. Calculate \( P(pass) \): \( P(pass) = \frac{Total \text{ number of students who passed}}{\text{Total number of students}} \)3. Calculate \( P(male) \times P(pass) \).4. Calculate \( P(male \text{ and } pass) \): \( P(male \text{ and } pass) = \frac{\text{Number of males who passed}}{\text{Total number of students}} \)5. Compare the two results to determine if they are equal. If they are, the events are independent; if not, they are dependent.6. Fill in the blanks in the given sentence with your findings and submit.#### Probability Equations:- \( P(male) = \frac{81 + 84}{81 + 84 + 70 + 5} \)- \( P(pass) = \frac{81 + 70}{81 + 84 + 70 + 5} \)- \( P(male) \times P(pass

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A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth. Passed Failed Male 81 84 Female 70 5 Since P(male)xP(pass): and

A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth. Passed Failed Male 81 84 Female 70 5 Since P(male)xP(pass): and

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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