103 LearnersLast updated on June 12th, 2025
Experimental Probability
Experimental probability is a mathematical concept that is used to estimate the likeliness of an event occurring. Here, the estimation is made based on actual experiments. In this topic, we will talk about experimental probability in detail.
What is Experimental Probability in Math?
Experimental probability is the probability which is calculated based on actual experiments. The process of randomly repeating an experiment to figure out its likelihood is known as a trial. The probability of an occurrence is calculated using the formula:
For example: When rolling a die 10 times, 5 appears 2 times, so we express the experimental probability of resulting in 5 as:
P (X) = Number of times event X occurs/Total number of trials
P(5) = 2/ 10 = 0.2
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Difference between Experimental and Theoretical Probability
Experimental probability and theoretical probability are two different types of probability. Let’s learn how they differ.
| Experimental Probability | Theoretical Probability |
| Probability derived from real-life experiments or observations | Derived using mathematical theories or assumptions. |
| Formula: P(E) = <formula> | Formula: P(E) = <formula> |
| Example: Rolling a die 15 times. The number 5 appeared 8 times. P(5) = 8/15 and P(number ≠ 5) = 7/15 |
A six-sided die is rolled once. P(5) = 1/6 and P(number ≠ 5) = 5/6 |
Tips and Tricks for Experimental Probability
Understanding experimental probability enables students to make predictions in real-world situations. Here are some tips and tricks to help you master the concept easily:
- Conduct multiple trials to obtain accurate results.
- Do not assume that the probability of past occurrences always influences future outcomes.
- Remember that the results will not be the same always as the trials are random.
- Record outcomes in an organized manner for effective analysis of the probability.
- As the number of trials increases, experimental probability becomes closer to the theoretical probability.
Common Mistakes and How to Avoid Them in Experimental Probability
Students might make mistakes when calculating the experimental probability. Take a look at some of the most common mistakes and how to avoid them.
Mistake 1
Insufficient Trials
They sometimes do not repeat the experiment as required, which can lead to inaccurate results.
For example: Rolling a die 5 times and getting a 6 twice. The likelihood of getting a 6 is 0.4, which is much higher than the theoretical probability.
Always repeat the experiment to increase the probability of the event, which will lead to accurate results.
Mistake 2
Experimental Probability Equals Theoretical Probability
They assume that simple experiments will always match the theoretical probabilities.
For e.g.,
tossing a coin several times and consistently getting tails can lead them to believe that it is more likely to get tails than heads.
Experimental probability completely depends on real-life experiments or trials, which will always differ each time.
Mistake 3
Confusion between Probability and Possibility
There is a common misconception that events with high probability are more likely to occur and vice versa. If a number did not appear in the first 5 trials, you cannot conclude that it is impossible to get that number. Always remember that probability is just chance, not assurance.
Mistake 4
Assuming Relative Frequency as Constant Probability
It is often seen that students assume experimental probability is the same for every trial in experiments.
For example: When they toss a coin 10 times, give a head 5 times(50%) and mistakenly assume that it is the same in every trial.
Keep in mind that probability can settle after a significant number of times.
Mistake 5
Misinterpretation in Real-life Situations
When we apply experimental probability in situations like weather forecasting, it may result in some errors.
For example, it is raining in a place for six days continuously in summer, which leads us to assume the entire summer will be rainy.
Ensure that the long-term data trends are used and not the short-term fluctuations for making accurate predictions.
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Real-Life Applications of Experimental Probability
Experimental probability is based on trials and outcomes and is widely applied in various fields. Here are some real-life applications:
- Scientists conduct clinical trials to determine the effectiveness and side effects of new medications.
- They can create a weather forecast report by making predictions about daily weather conditions.
- The experimental probability enables students to estimate the scores in sports based on past occurrences.
- It is an effective way to conduct classroom surveys and analyze how likely it is to get a common response.
- They can assess the right time to invest money by predicting stock prices based on past trends.
Solved Examples of Experimental Probability
Problem 1
A six-sided die is rolled 320 times, and the number 4 appears 55 times. Find the experimental probability of rolling a 4.
The experimental probability of getting 4 is 0.17.
Explanation
We have the total number of trials: 320
Number of times: 55
Now, we use the formula: Number of times an event occurs ÷ Total number of trials.
P (4) = 55/320 = 0.171875
Therefore, the experimental probability of getting 4 is 0.1719.
Problem 2
A bag contains green and blue balls. A person randomly draws a ball, notes the color, and replaces it. After 120 trials, 50 were red. What is the experimental probability of drawing a green ball?
The experimental probability of obtaining a green ball is 0.41.
Explanation
We have the total number of trials:120
Given the number of times, green was obtained: 50
Now we use the formula:
Probability = Number of times an event occurs ÷ Total number of trials.
P(Green) = 50/120 = 0.41
Therefore, the experimental probability of obtaining a green ball is 0.41.
Problem 3
Imagine you toss a coin 100 times, and tails appear 30 times. Calculate the experimental probability of getting tails.
The experimental probability of obtaining tails is 0.3.
Explanation
Given, the total number of trials = 100
Out of which, the number of times tails obtained = 30
Here, we use the formula:
Probability = Number of times an event occurs ÷ Total number of trials
P (Tails) = 30/100 = 0.3
Therefore, the experimental probability of obtaining tails is 0.3.
Problem 4
A teacher is early to school 10 times a month (out of 23 school days). What is the experimental probability of the teacher being early?
The experimental probability is 0.43.
Explanation
Here, the total school days are equal to the number of trials: 23
Number of times: 10
Now, we use the formula:
Probability = Number of times an event occurs ÷ Total number of trials
P(Early) = 10/23 = 0.435
Therefore, the experimental probability is 0.43.
Problem 5
A basketball player takes 200 free throws and makes 90. What is the experimental probability of scoring a basket?
The experimental probability is 0.45
Explanation
Here, the number of trials is equal to the free throws = 200
Event occurs (shots) = 90
Using the formula:
Probability = Number of times an event occurs ÷ Total number of trials
P(Scoring) = 90/200 = 0.45
Therefore, the experimental probability is 0.45.
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FAQs on the Experimental Probability
1.What do you mean by probability?
2.What are the two types of probability?
3.Give one real-life example of experimental probability.
4.State one difference between experimental probability and theoretical probability.
5.Does the experimental probability predict the occurrence of an event?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
