Skip to main content
Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.1.25
Chapter 3, Problem 3.1.25

Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.
25. Guessing the initial of a student's middle name

Verified step by step guidance
1
Step 1: Understand the problem. The task involves identifying the sample space for a probability experiment where you guess the initial of a student's middle name. The sample space consists of all possible outcomes for the experiment.
Step 2: Define the sample space. The sample space includes all letters of the English alphabet, as these are the possible initials for a middle name. Represent this as {A, B, C, ..., Z}, where each letter corresponds to a possible outcome.
Step 3: Determine the number of outcomes in the sample space. Since there are 26 letters in the English alphabet, the number of outcomes in the sample space is 26.
Step 4: Draw a tree diagram if needed. A tree diagram can visually represent the sample space. Start with a single point (the start of the experiment) and branch out into 26 branches, each labeled with a letter from A to Z.
Step 5: Summarize the findings. The sample space consists of 26 outcomes, each corresponding to a letter of the English alphabet. The tree diagram provides a visual representation of these outcomes.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

Key Concepts

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

Sample Space

The sample space in a probability experiment is the set of all possible outcomes. For example, when guessing the initial of a student's middle name, the sample space consists of all 26 letters of the English alphabet. Understanding the sample space is crucial for calculating probabilities and determining the likelihood of various outcomes.
Recommended video:
05:11
Sampling Distribution of Sample Proportion

Outcomes

An outcome is a specific result of a probability experiment. In the context of guessing a middle name's initial, each letter from A to Z represents a distinct outcome. The total number of outcomes in the sample space directly influences the probability calculations for any event derived from the experiment.
Recommended video:
Guided course
06:00
The Binomial Experiment

Tree Diagram

A tree diagram is a visual representation used to illustrate all possible outcomes of a probability experiment. It branches out from a starting point, showing each possible outcome at each stage. In this case, a tree diagram could simply list the letters A through Z, helping to visualize the sample space and the number of outcomes effectively.
Recommended video:
5:14
Probability of Mutually Exclusive Events
Related Practice
Textbook Question

Using a Pie Chart to Find Probabilities In Exercises 83-86, use the pie chart at the left, which shows the number of workers (in millions) by occupation for the United States. (Source: U.S. Bureau of Labor Statistics)

84. Find the probability that a worker chosen at random is not employed in a service occupation.

" style="" width="260">

Textbook Question

34. Lottery Number Selection A lottery has 52 numbers. In how many different ways can six of the numbers be selected? (Assume the order of selection is not important.)

Textbook Question

25. Playlist A band is preparing a setlist of 21 songs for a concert. How many different ways can the band play the first six songs?

Textbook Question

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.

46. Event F: rolling a number divisible by 5

Textbook Question

True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false,

explain why.

4. When two events are independent, they are also mutually exclusive.

Textbook Question

Graphical Analysis In Exercises 7 and 8, determine whether the events shown in the Venn diagram are mutually exclusive. Explain your reasoning.