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251 LearnersLast updated on November 25, 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, also called empirical probability, is the probability found by actually performing an experiment and observing outcomes. Each repetition of the experiment is known as a trial.
The experimental probability of an event E is given by:
\( P(E) = \frac{\text{Number of times event } E \text{ occurs}}{\text{Total number of trials}} \)
For example, a coin is flipped 50 times and lands on heads 28 times.
Total number of trials = 50
Number of times head occurs = 28
So, the experimental probability of getting heads is: P (head) \(= {28 \over 50 }= 0.56\)
Therefore, the experimental probability of getting heads is 56%.
Difference Between Experimental and Theoretical Probability
Theoretical and experimental probability describe how likely an event is, but they differ in how they calculate probability. Here, we will learn the difference between experimental and theoretical probability.
| Experimental Probability | Theoretical Probability |
| Experimental probability is determined by conducting experiments or trials and observing how often the event occurs. | Theoretical probability calculates the chance of an event by assuming all possible outcomes are equally likely. |
| Based on the actual experiments or trials. | Based on mathematical analysis and reasoning. |
| \( P(E) = \frac{\text{Number of times event } E \text{ occurs}}{\text{Total number of trials}} \) | \( P(E) = \frac{\text{Number of favorable outcomes } \text{ }}{\text{Total number possible outcomes}} \) |
| Accuracy can vary based on the sample size, experimental error, etc. | More accurate and stable. |
| Used in real-world applications when we have data from experiments. | Used in theoretical models, predictions, and when all possible outcomes are known. |
| For example, toss a coin 50 times and heads appear 28 times. Then the probability of getting a head is \({28\over50 }= 0.56\) | For example, the probability of heads for a fair coin is \({1 \over 2}= 0.5\) |
Experimental Probability Formula
Experimental probability helps us understand the probability of an event by looking at what actually happens in repeated trials. The experimental probability formula is:
\(\text{P(E)} = \frac{\text{Number of times an event occurs in an experiment}}{\text{Total number of trials}}\)
For example, a die is rolled 40 times, and the number 6 appears 9 times.
Here,
The total number of trials = 40
Favorable events = 9
The experimental probability of rolling a 6 is: \(P(6) = {9\over 40 }= 0.225\)
So, the experimental probability that the die landed on 6 is 0.225 or 22.5%.
You, 16:56
Tips and Tricks for Experimental Probability
Experimental probability becomes much easier to understand when learners practice, record outcomes correctly, and compare results with theoretical probability. Here are some tips and tricks to master experimental probability.
- Always remember that the accuracy of experimental probability improves when you repeat an experiment many times. More trials help the results move closer to the expected probability.
- Parents can use real-life examples to teach students about experimental probability—for example, the chance of running, the possibility of getting a red candy in a pack.
- Encourage students to use experimental probability worksheets to practice.
- Teachers can help students organize their data using tally marks, charts, or simple spreadsheets.
- Avoid assuming the answer based on the previous events, as each trial is independent.
- Students can use experimental probability calculators to verify their results.
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 improve accuracy and reliability of the results.
Mistake 2
Experimental Probability Equals Theoretical Probability
They assume that simple experiments will always match the theoretical probabilities.
For example, 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.
Real-Life Applications of Experimental Probability
Experimental probability is used whenever theoretical chances are unknown or unreliable. Here are some real-life applications of experimental probability.
- In weather forecasting, meteorologists use experimental probability to predict the chance of rain or snow. For example, if rain appears in 70 out of 100 simulations, then the experimental probability of rain is 70%.
- Experimental probability is used in manufacturing for quality control. For example, a factor tests 100 light bulbs and finds four defective ones. The probability that a randomly selected bulb is defective \(= 4 ÷ 100 = 0.04\).
- In medical and clinical trials, experimental probability is used to determine if the drug is effective enough to be approved.
- Experimental probability to analyze traffic patterns. By observing traffic flow at specific times and locations, they can estimate the likelihood of congestion and better plan traffic management systems.
- In sports, experimental probability helps predict outcomes, such as a team's chances of winning a match based on previous games.
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 0.172.
Explanation
We have the total number of trials: 320
Number of times: 55
Now, we use the formula: \( \text{Probability} = \frac{\text{Number of times an event occurs}}{\text{Total number of trials}} \)
\(P (4) = 55 ÷ 320 = 0.171875 ≈ 0.172\)
Therefore, the experimental probability of getting 4 is 0.172.
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 green. 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:
\(\text{Probability} = \frac{\text{Number of times an event occurs}}{\text{Total number of trials}} \)
\(P(Green) = 50 ÷ 120 \\ \ \\ = 0.41 \)
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:
\( \text{Probability} = \frac{\text{Number of times an event occurs}}{\text{Total number of trials}} \)
\(P (Tails) = 30 ÷ 100 \\ \ \\ = 0.3\)
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:
\(\text{Probability} = \frac{\text{Number of times an event occurs}}{\text{Total number of trials}} \)
\(P(Early) = 10 ÷ 23 \\ \ \\ = 0.435\)
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:
\(\text{Probability} = \frac{\text{Number of times an event occurs}}{\text{Total number of trials}} \)
\(P(Scoring) = 90 ÷ 200 \\ \ \\ = 0.45\)
Therefore, the experimental probability is 0.45.
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?
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!
