Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 35m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 0m

4. Probability

Addition Rule

Statistics

4. Probability

Addition Rule

Previous problemNext problem

1:42 minutes

Problem 3.RE.25

Textbook Question

In Exercises 25 and 26, determine whether the events are mutually exclusive. Explain your reasoning.
25. Event A: Randomly select a red jelly bean from a jar.
Event B: Randomly select a yellow jelly bean from the jar.

Verified step by step guidance

Understand the concept of mutually exclusive events: Two events are mutually exclusive if they cannot occur at the same time. In other words, the occurrence of one event means the other cannot happen.

Identify the events in the problem: Event A is selecting a red jelly bean, and Event B is selecting a yellow jelly bean.

Consider the scenario: If you randomly select one jelly bean from the jar, it can only be one color at a time. A single jelly bean cannot simultaneously be red and yellow.

Analyze the relationship between the events: Since selecting a red jelly bean (Event A) and selecting a yellow jelly bean (Event B) cannot happen at the same time, the two events are mutually exclusive.

Conclude your reasoning: Based on the analysis, the events are mutually exclusive because the selection of one color excludes the possibility of selecting the other color in a single draw.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mutually Exclusive Events

Mutually exclusive events are those that cannot occur at the same time. In probability, if one event happens, the other cannot. For example, when rolling a die, the events of rolling a 2 and rolling a 5 are mutually exclusive because both cannot happen simultaneously.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. In the context of selecting jelly beans, the sample space includes all the different colored jelly beans in the jar. Understanding the sample space helps in determining the likelihood of various events occurring.

Probability

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1. In this scenario, calculating the probability of selecting a red or yellow jelly bean involves understanding how many of each color are present in the jar relative to the total number of jelly beans.

Watch next

Master Probability of Mutually Exclusive Events with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

25. Working from Home The table shows the results of a survey that asked 1811 people how often they work from home. A person is selected at random from the sample. Find the probability of each event.

b. The person is female or does not work from home.

" style="" width="400">

views

Textbook Question

26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.

a. The person wears only contacts or only glasses.

" style="" width="480">

views

Textbook Question

d. The person is male or does not wear glasses.

" style="max-width: 100%; white-space-collapse: preserve;" width="480">

views

Textbook Question

29. Explain, in your own words, why in the Addition Rule for P(A or B or C), P(A and B and C) is added at the end of the formula.

views

Textbook Question

28. A sample of 6500 automobiles found that 1560 of the automobiles were black, 3120 of the automobiles were sedans, and 1170 of the automobiles were black sedans. Find the probability that a randomly chosen automobile from this sample is black or a sedan.

views

Textbook Question

In Exercises 29-32, find the probability.

31. A 12-sided die, numbered 1 to 12, is rolled. Find the probability that the roll results in an odd number or a number less than 4.

views

Textbook Question

In Exercises 33 and 34, use the pie chart at the left, which shows the percent distribution of the number of students in U.S. public schools in a recent year. (Source: U.S. National Center for Education Statistics)

" style="" width="200">

34. Find the probability of randomly selecting a school with 300 or more students.

views

Textbook Question

39. You are given that P(A) = 0.15 and P(B) = 0.40. Do you have enough information to find P(A or B)? Explain.

views

Show more practices

Download the Mobile app

Privacy

Do not sell my personal information

Accessibility

Patent notice

Sitemap

In Exercises 25 and 26, determine whether the events are mutually exclusive. Explain your reasoning.25. Event A: Randomly select a red jelly bean from a jar.Event B: Randomly select a yellow jelly bean from the jar.

Key Concepts

Mutually Exclusive Events

Sample Space

Probability

Watch next

In Exercises 25 and 26, determine whether the events are mutually exclusive. Explain your reasoning.
25. Event A: Randomly select a red jelly bean from a jar.
Event B: Randomly select a yellow jelly bean from the jar.