Choose the answer to both correctly and read carefully. Deals with two way tables Venn diagram and probability. ### Understanding Probability with HeadlinesA civics teacher asked her students to indicate whether they believed each of two headlines. One headline was false and the other was true, but the students did not know this. Here are the probabilities based on the survey results:- **90%** of the students believed the true headline.- **82%** of the students believed the false headline.- **75%** of the students believed both headlines.#### QuestionIn this sample, are the events "believed the false headline" and "believed the true headline" mutually exclusive?**Choose 1 answer:**- **A** Yes- **B** No#### Probability CalculationCalculate the probability that a randomly selected person from this sample believed the true headline *or* believed the false headline.\[ P(\text{believed true OR believed false}) = \]---### ExplanationIn probability, mutually exclusive events cannot happen at the same time. Since 75% of the students believed both headlines, these two events are not mutually exclusive.

Given P(true headline)= 0.90, P(false headline)=0.82, P( true headline and false headline)=0.75

Answered: Choose the answer to both correctly and…

Math

Probability

Choose the answer to both correctly and read carefully. Deals with two way tables Venn diagram and probability.

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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Question

Choose the answer to both correctly and read carefully. Deals with two way tables Venn diagram and probability.

### Understanding Probability with Headlines

A civics teacher asked her students to indicate whether they believed each of two headlines. One headline was false and the other was true, but the students did not know this. Here are the probabilities based on the survey results:

- **90%** of the students believed the true headline.
- **82%** of the students believed the false headline.
- **75%** of the students believed both headlines.

#### Question

In this sample, are the events "believed the false headline" and "believed the true headline" mutually exclusive?

**Choose 1 answer:**

- **A** Yes
- **B** No

#### Probability Calculation

Calculate the probability that a randomly selected person from this sample believed the true headline *or* believed the false headline.

\[ P(\text{believed true OR believed false}) = \]

---

### Explanation

In probability, mutually exclusive events cannot happen at the same time. Since 75% of the students believed both headlines, these two events are not mutually exclusive.

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