Theoretical and experimental probability answer key

Q: What is an example of theoretical and experimental probability?

For example, if a dice is rolled 6000 times and the number 5 occurs 990 times, then the experimental probability that 5 shows up on the dice is 990/6000 = 0.165. For example, the theoretical probability that the number 5 shows up on a dice when rolled is 1/6 = 0.167.

The following table highlights the difference between Experimental Probability and Theoretical Probability. Scroll down the page for more examples and solutions.

Table of Contents Show

How To Find The Experimental Probability Of An Event?
How To Find The Theoretical Probability Of An Event?
What Is The Theoretical Probability Formula?
Comparing Theoretical And Experimental Probability
What is an example of theoretical and experimental probability?
What is the theoretical probability of rolling a 4?
What was the experimental probability of rolling a 4?

How To Find The Experimental Probability Of An Event?

Step 1: Conduct an experiment and record the number of times the event occurs and the number of times the activity is performed.

Step 2: Divide the two numbers to obtain the Experimental Probability.

How To Find The Theoretical Probability Of An Event?

The Theoretical Probability of an event is the number of ways the event can occur (favorable outcomes) divided by the number of total outcomes.

What Is The Theoretical Probability Formula?

The formula for theoretical probability of an event is

One way to find the probability of an event is to conduct an experiment.

Example:
A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the experimental probability of getting a blue marble.

Solution:
Take a marble from the bag.
Record the color and return the marble.
Repeat a few times (maybe 10 times).
Count the number of times a blue marble was picked (Suppose it is 6).

The experimental probability of getting a blue marble from the bag is

How to find and use experimental probability?

The following video gives another example of experimental probability.

How the results of the experimental probability may approach the theoretical probability?

Example:
The spinner below shows 10 equally sized slices. Heather spun 50 times and got the following results.
a) From Heather’s' results, compute the experimental probability of landing on yellow.
b) Assuming that the spinner is fair, compute the theoretical probability of landing in yellow.

We can also find the theoretical probability of an event.

Example:
A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the theoretical probability of getting a blue marble.

Solution:
There are 8 blue marbles. Therefore, the number of favorable outcomes = 8.
There are a total of 20 marbles. Therefore, the number of total outcomes = 20

Example:
Find the probability of rolling an even number when you roll a die containing the numbers 1-6. Express the probability as a fraction, decimal, ratio and percent.

Solution:
The possible even numbers are 2, 4, 6.
Number of favorable outcomes = 3.
Total number of outcomes = 6

The probability =(fraction) = 0.5 (decimal) = 1:2 (ratio) = 50% (percent)

Comparing Theoretical And Experimental Probability

The following video gives an example of theoretical and experimental probability.

Example:
According to theoretical probability, how many times can we expect to land on each color in a spinner, if we take 16 spins?
Conduct the experiment to get the experimental probability.

We will then compare the Theoretical Probability and the Experimental Probability.

The following video shows another example of how to find the theoretical probability of an event.

Examples:

A spinner is divided into eight equal sectors, numbered 1 through 8.
a) What is the probability of spinning an odd numbers?
b) What is the probability of spinning a number divisible by 4?
b) What is the probability of spinning a number less than 3?
A spinner is divided into eight equal sectors, numbered 1 through 8.
a) What is the probability of spinning a 2?
b) What is the probability of spinning a number from 1 to 4?
b) What is the probability of spinning a number divisible by 2?

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The following figure compares experimental and theoretical probability. Scroll down the page for more examples and solutions.

Experimental and Theoretical Probability
This video defines and uses both experimental and theoretical probabilities.
Example:
1. A player hit the bull's eye on a circular dart board 8 times out of 50. Find the experimental probability that the player hits a bull's eye.
2. Find the theoretical probability of rolling a multiple of 3 with a number cube.
3. Brown is a dominant eye color for human beings. If a father and mother each carry a gene for brown eyes and a gene for blue eyes, what is the probability of their having a child with blue eyes?
Experimental and Theoretical Probability
Understand and compare experimental and theoretical probability
Example:
a) Find the theoretical probability of obtaining doubles when rolling two number cubes.
b) What is the experimental probability of roling doubles for 20 trials, when you get 3 doubles in the 20 trials?
Experimental Probability (Surveys)
Learn to find probability from experimental data from surveys
Example:
1. A reporter surveys 65 people to determine whether they plan to vote for or against a proposed amendment.
a) What is the experimental probability that the next person surveyed would say he or she plans to vote the amendment?
b) What is the experimental probability that the next person surveyed would say he or she plans to vote against the amendment?
2. The table shows the high temperature recorded on June 28 in Miami, Florida over an eight-year period. What is the experimental probability that the high temperature on June 28, 2008 will be below 90°C? Finding Theoretical Probability
In this video, we will learn to find the theoretical probability, or chance, of an event occurring.
Examples:
A. What is the theoretical probability that the spinner will land on 2?
B. What is the probability of randomly choosing a vowel from the letters A, B, C, D, and E?
C. Nine pieces of paper with the numbers 1,2,2,3,4,4,5,6, and 6 printed on them are placed in a bag. A student chooses one without looking. Compare the probability of choosing the number 1 with that of choosing the number 4.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

What is an example of theoretical and experimental probability?

For example, if a dice is rolled 6000 times and the number '5' occurs 990 times, then the experimental probability that '5' shows up on the dice is 990/6000 = 0.165. For example, the theoretical probability that the number '5' shows up on a dice when rolled is 1/6 = 0.167.