1147 LearnersLast updated on June 18th, 2025
Terms in Probability
The possibility of an event taking place is measured with the help of probability. Mathematically, it can be defined as the ratio of the possible number of favorable outcomes to the total count of events. Now let’s discuss some important terms in probability. Experiment: An experiment is an activity or action whose result is unknown. All the events have favorable and unfavorable outcomes. For example, rolling a die. Sample Space (S): The sample space is the set of all possible outcomes of the experiment. For e.g., the possible outcomes of rolling a die are 1, 2, 3, 4, 5, and 6. Therefore, the sample space (S) can be written as S = {1, 2, 3, 4, 5, 6} Events (E): An event is the subset of a sample space which has a clearly defined outcome. For example, rolling an even number {2, 4, 6}
Probability of an Event (P(E)):
The chance that a specific event will occur. It is the number of ways something can happen divided by the number of possible outcomes. For example, the probability of rolling an even number is the number of favorable outcomes / total number of outcomes
Number of favorable outcomes = 3
Total number of outcomes = 6
Thus P(E) = 3/6 = 0.5
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Types of Events:
There are different types of events in probability. Some important types of events are listed below
Independent Event:
In independent events, two events are said to be independent when the occurrence of one does not affect the occurrence of the other. For example, rolling a die and tossing a coin are two separate events that do not affect each other’s results.
Dependent Event:
Two events are dependent when the outcome of an event is affected by the outcome of another event. For e.g., pulling out two cards from a deck with no replacement.
Mutually Exclusive Event:
Two events are said to be mutually exclusive if they cannot take place concurrently. For example, rolling a 3 and 5 on a single six-sided die. The events are mutually exclusive as they cannot occur together.
Complementary Event:
Complementary event is the opposite of the given event. The sum of the probabilities of the event and its complement is always 1.
For e.g., let's say today the probability of rain is 0.7. Therefore the probability of no rain is 1 minus probability of rain. So, probability of no rain = 1 - 0.7 = 0.3.
Certain Event:
The event that is guaranteed to happen, here p(E) is 1.
Impossible Event:
The impossible event is an event that can never happen, where P(E) = 0.
Conditional Probability:
It is the probability of event A occurring when event B has already happened. Conditional probability is found using the formula, P(A|B) = P(A∩B) / P(B), where P(B) ≠ 0.
Probability Distribution:
It indicates the probabilities of every possible outcome of a particular event.
Theoretical vs. Experimental Probability:
The theoretical probability is calculated using formulas based on the possible outcomes. Experimental probability is calculated using the actual experiment.
Bayes' Theorem:
It is used to calculate the conditional probability of event A after the occurrence of event B.
Law of Large Numbers:
The law of large numbers states that as the number of trials increases, the experimental probability will get closer to the theoretical probability.
Real-World Applications Of Terms in Probability
In the real world, we use probability in different ways, such as weather forecasting, medical diagnostics, market research, and many more. Let’s learn a few applications of probabilities.
- To find the probability of getting heads or tails when flipping a coin
- To find the probability of getting a specific card when drawing a card from a deck of cards
- In medical diagnosis, it is to determine the probability that a patient has a disease when the result is positive.
- To predict weather changes, we use probability.
Common Mistakes and How To Avoid Them in Terms of Probability
Students make mistakes when working with terms in probability. Let’s learn a few common mistakes and ways to avoid them.
Mistake 1
Confusing independent and dependent events
Students think that events occurring sequentially are automatically independent. But if the outcome of one event changes the probability of the other, then the event is dependent. So, to avoid it, understand the concept of independent and dependent events.
Mistake 2
Ignoring the sample space
Sometimes, students fail to list all the possible outcomes that can lead to errors in calculation. Always verify and double-check the sample space to verify that the sum of the probabilities for all the outcomes is 1; then, the sample space is correct.
Mistake 3
Not understanding mutually exclusive events
The students assume that any two events cannot occur together. If there are no common outcomes, then the event is mutually exclusive. That means the events are not mutually exclusive if they share the same outcomes.
Mistake 4
Thinking all probabilities are equal
Students think that every outcome is the same, but this is not true; many outcomes can be weighted. So, check if the experiment is truly fair and if the condition is biased, and then adjust the probability calculation accordingly.
Mistake 5
Confusing complementary events
Mixing up with the event and complementary events is common among students. So students should remember that the sum of the complementary event and probability of the event should be 1, P(A) + P(A') = 1
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Solved Examples of Terms in Probability
Problem 1
Two fair coins are tossed. What is the probability that both coins land on heads?
The probability that both the coins will land heads is ¼
Explanation
The probability is calculated using the following formula;
The number of favorable outcomes/the number of outcomes
The probability of getting heads on one toss = ½
The tosses are independent; the joint probability that both coins land on heads is
P(H₁ and H₂) = P(H₁) × P(H₂)
=½ × ½ = ¼
Problem 2
A bag contains 5 red and 3 blue balls. If two balls are drawn one after the other without replacement, what is the probability that both are red?
The probability of drawing two red balls in succession without replacement is 5/14
Explanation
Total number of balls = 8
Number of red balls = 5
The probability of drawing a red ball is (P (red1)) = ⅝
In the second draw;
After one red ball is drawn, 4 red balls remain out of a total of 7 balls:
P (red2 | red1) = 4/7
Multiply the two probabilities: P(both red) = ⅝ × 4/7
= 20/56 = 5/14
Problem 3
A single card is drawn from a standard 52-card deck. Given that the card drawn is a face card (Jack, Queen, or King), what is the probability it is a King?
The probability of getting a king is 1/3
Explanation
The total number of face cards in the deck = 12
The probability that a face card is a king is = number of kings/total face cards
= 4/12 = 1/3
Problem 4
When rolling a six-sided die, what is the probability of getting either a 2 or a 5?
The probability of getting either a 2 or 5 is 1/3
Explanation
The total number of outcomes = 6
The probability of rolling a 2 is ⅙
The probability of rolling a 5 is ⅙
As these events are mutually exclusive, adding the probabilities = ⅙ + ⅙ = 2/6 = ⅓
Problem 5
How many ways can 4 people be arranged in a row?
The number of arrangements of 4 people is 24
Explanation
The number of arrangements of 4 people is given by the factorial of 4
That is 4! = 4 × 3 × 2 × 1 = 24
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FAQs on Terms in Probability
1.What is probability?
2.What are random experiments?
3.What is an event in probability?
4.How is the probability of an event calculated?
5.What is a complementary 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!
