Textbook Question
In computing classical probabilities, all outcomes must be equally likely. Explain what this means.
60
views
4. Probability
Basic Concepts of Probability
1:07 minutesProblem 5.1.1e
Textbook Question
Define each of the following.
e. Equally likely outcomes
Verified step by step guidance1
Understand that 'equally likely outcomes' refers to a situation in probability where each possible outcome of an experiment has the same chance of occurring.
Recognize that if there are \(n\) possible outcomes, and they are equally likely, then the probability of each outcome is \(\frac{1}{n}\).
Express this formally: if \(S\) is the sample space with \(n\) outcomes, then for each outcome \(s_i \in S\), \(P(s_i) = \frac{1}{n}\).
Note that this concept is fundamental in classical probability, where the assumption of equally likely outcomes simplifies the calculation of probabilities.
Remember that this definition applies only when no outcome is favored over another, such as rolling a fair die or flipping a fair coin.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Equally Likely Outcomes
Equally likely outcomes refer to events in a probability experiment that have the same chance of occurring. For example, when rolling a fair six-sided die, each face (1 through 6) is an equally likely outcome because each has a probability of 1/6.
Recommended video:
Guided course
06:00
The Binomial Experiment
Sample Space
The sample space is the set of all possible outcomes of a probability experiment. Understanding the sample space helps identify which outcomes are equally likely and is essential for calculating probabilities.
Recommended video:
05:11Sampling Distribution of Sample Proportion
Probability
Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. When outcomes are equally likely, the probability of an event is the ratio of favorable outcomes to the total number of outcomes in the sample space.
Recommended video:
5:37Introduction to Probability
Related Videos
Related Practice