1132 LearnersLast updated on June 18th, 2025
Random Experiments
The activities or the events where the result is unknown are the experiments. A random experiment is an event or an activity where the outcome can be one or more and cannot be predictable. In this topic, we will learn more about random experiments, methods to analyze them, applications, and so on.
What are Random Experiments in Probability?
Probability theory itself is based on random experiments. Although the outcomes are unpredictable, random experiments are often repeated several times under the same conditions. A random experiment is part of the probability theory and the conditions to be fulfilled are:
Random experiments should be repeated several times under the same conditions
The outcome cannot be predicted in a random experiment.
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How to Find the Probability of Random Experiments?
Probability is a mathematical concept used to predict the likeliness of an event. The calculation is done by comparing the number of methods an event can happen to the number of possible outcomes. Follow the given steps to find the probability of random experiments.
Step 1: Identifying the sample space. The sample space is all possible outcomes of the experiments.
For example, when a fair coin is tossed twice, we want to find the probability of getting exactly two heads. As the result of tossing a coin is either heads (H) or tails (T), the possible outcomes are
{HH, HT, TH, TT}; so the total number of possible outcomes is 4.
Step 2: Identify the favorable outcomes
Here, the favorable outcome is HH, so the number of favorable outcomes is 1
Step 3: Apply the formula of probability
Probability = number of favorable outcomes/total number of possible outcomes
Here, the number of favorable outcomes = 1
The total number of possible outcomes = 4
P(exactly two heads) = ¼ = 0.25
Real-world applications of Random Experiments
In various fields in our daily lives, we use random experiments. Now, let’s learn some applications of random experiments.
- In finance, for the stock market analysis and in forecasting the asset price, we use random experiments.
- For quality control in manufacturing industries, we use random experiments.
- When designing games and simulation where the outcomes are determined by random processes like rolling dice or drawing cards
Common Mistakes and How to Avoid Them in Random Experiments
Mistakes are common among students when working on random experiments, mostly, they make the same errors. Take a look at some of the common mistakes and methods to avoid them, so that we can be wary of them.
Mistake 1
Using an insufficient sample size
When collecting data, students tend to use a sample size that will increase the risk of missing a real effect. So, it is important to calculate the required sample size before starting.
Mistake 2
Incorrect randomization
Incorrect randomization can lead to systematic errors and imbalanced groups. The preexisting difference can bias the result if the experiment is not truly random. So, stratified randomization should be used to balance them in groups.
Mistake 3
Selection bias
Selection bias occurs when the population is large and the sample size is not representative. It mostly occurs when the process is not random or the participants are chosen by convenience. So, to avoid this, give an equal chance of selection to all the members of the population and try to use sampling techniques to improve the representativeness.
Mistake 4
Not repeating trials
Not repeating trials in a random experiment can make it hard to know if the result is reliable or not. Confidence in the results increases if we repeat the experiment. So, to avoid this error, try to repeat the experiment several times to verify the consistency of the experiment.
Mistake 5
Making errors while listing the data
Mistakes while listing the data can lead to errors in the results and incorrect conclusions. So always double-check the entries after the collection of data.
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Solved Examples of Random Experiments
Problem 1
What is the probability of getting an even number when a fair six-sided die is rolled?
The probability of an even number is ½
Explanation
Even numbers in a six-sided die = 2, 4, and 6
Since there are 3 even numbers in six possible outcomes,
Probability = number of favorable outcomes / total outcomes
= 3/6 = 1/2
Problem 2
A fair coin is tossed once. What is the probability of getting heads?
The probability of getting heads is 1/2
Explanation
The possible outcomes: head and tail
The probability of getting heads = ½
Problem 3
A bag contains 3 red, 4 blue, and 5 green balls. A ball is picked randomly. What is the probability of picking a blue ball?
1/3 is the probability of picking up a blue ball
Explanation
Total number of balls = 12
The number of blue balls = 4
The probability of getting a blue ball = number of favorable outcomes / total outcomes
= 4/12 = 1/3
Problem 4
A card is taken out from a deck of 52 cards. What is the probability of drawing a king?
The probability of drawing a king is 1/13
Explanation
The total number of cards = 52 cards
The number of favorable outcomes = 4 cards
The probability of getting a king = number of favorable outcomes / total outcomes
= 4/52 = 1/13
Problem 5
A number is randomly selected from 1 to 10. What is the probability of selecting a prime number?
The probability of choosing a prime number is 2/5
Explanation
The total outcomes = 10
The favorable outcomes = 4 {2, 3, 5, 7}
Total numbers = 10
Prime numbers = 2, 3, 5, and 7
So, probability = number of favorable outcomes / total outcomes
= 4/10 = 2/5
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FAQs on Random Experiments
1.What is a random experiment?
2.What is sample space?
3.What is an event in the context of a random experiment?
4.How is the probability of a random experiment calculated?
5.What is an independent 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!
