Types of probability are one of the most important topics of mathematics. It is present in the curriculum of lower as well as higher classes. Because it helps us in many ways, like from solving mathematics problems to a real-life situation.
The probability is everywhere. Let’s take a few examples of it.
- Planning about the weather
Meteorologists use various instruments to predict whether it will rain or not on a particular day.
For instance, if it is said that there is a 60% chance of rain, it means that 60 out of 100 days would be the chance of rain. Therefore, it would be better to wear rain shoes instead of sandals.
- Sports Strategies
Coaches and Athletes use probability concepts to examine the best sports strategies for the competitions and games. A cricket coach estimates the batting average of the player when he lines up the players.
For instance, the player that has a 200 batting average signifies that the player hit 2 out of each 10 at the bat. At the same time, the player with a 400 batting average has more tendency to hit the ball- 4 out of every 10 balls.
What Is Probability?
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So you might have a little bit of idea about probability really is, but keeping that aside as we will discuss what probability means.
Probability = Possibility; in the short term, the possibility of getting something done or the possibility of solving some problem or the possibility of doing something. And also, there are different types of probability which we will be discussing below.
Terms Related To Probability
There are various terms for probability, here we will discuss few of them :
An event refers to an outcome or set of random experiment outcomes. It can be a single outcome or a combination of outcomes.
2. Sample Space
The sample space is the set of all possible outcomes of a random experiment. It represents the complete set of events that could potentially occur.
An experiment is a process or an activity that results in an outcome. In the context of probability, it refers to a situation where the outcome is uncertain or random.
4. Independent Events
If one event happens or does not happen, it does change the chance that the other will happen. Independent events are events where the occurrence or non-occurrence of one event does not affect the probability of the other event. The outcomes of independent events are statistically unrelated.
5. Dependent Events
Dependent events are ones whose chances of happening depend on how often another event happens. The outcomes of dependent events are statistically related.
6. Expected Value
The expected value is the average of a random variable’s values, weighted by how likely each value is. It represents the long-term average outcome of an experiment.
Applications Of Probability
Here are some applications of probability explained in simple language:
1. Risk Assessment
Probability is essential in assessing risks in various fields. Insurance companies use probability to calculate premiums by considering the likelihood of an event occurring and its potential costs. Similarly, in finance, probability is used to evaluate investment risks and make informed decisions.
2. Medical Diagnoses
In healthcare, probability is used to evaluate the likelihood of diseases or conditions based on symptoms, test results, and patient history. Doctors use probabilistic reasoning to diagnose and determine the most appropriate treatment options.
3. Quality Control
Probability is used in manufacturing and quality control processes. It helps determine the probability of defects or errors occurring during production and allows companies to identify and address potential issues before they become significant problems.
4. Genetics and Biology
Probability is used in genetics to study the likelihood of specific traits or diseases being passed down from parents to offspring. It is also used in biological experiments to analyze the probability of certain outcomes or events occurring.
5. Traffic Planning
Probability is used in traffic planning and engineering to estimate the flow of vehicles and analyze the likelihood of traffic congestion at different times and locations. This information helps in designing efficient road systems and managing traffic effectively.
Why Probability Is Important?
Here are five points explaining why probability is important:
- Probability allows us to assess and manage risks effectively, guiding decision-making processes and enabling us to allocate resources wisely.
- It forms the foundation of statistical analysis, enabling researchers to draw valid conclusions from data, make predictions, and understand complex phenomena.
- Probability provides a framework for making informed decisions in various fields, including finance, healthcare, and engineering, by quantifying uncertainties and evaluating potential outcomes.
- It plays a crucial role in scientific research, helping scientists design experiments, analyze data, and draw reliable conclusions about the natural world.
- Probability is essential in predictive modeling, enabling the estimation of future events and outcomes, leading to improved planning, forecasting, and decision-making in diverse domains.
What Is The Value Of Probability?
As we have discussed above, it is one of the most important mathematics branches, and it deals with the occurrence of random events. Probability helps understand some events that occur or not or the percentage of occurrence of that particular event.
The value of probability for occurring of a random event is always expressed between 0 and 1, so basically, from all this above information, we can say that the probability was introduced in mathematics for getting to know about the occurrence of some events. Or we can say that it helps us predict how likely events will happen.
Some Key Points About Probability
There is a basic theory associated with branch probability of random method. The meaning of probability is the chances of something likely to happen. This is the same thing as above, and that is the possibility of occurrence of an event. And all and all, this is also the probability theory used in the theory of probability distribution.
In the probability distribution theory, you will check that the probability of some outcome from any random experiment is based on the probability of any single element occurring from the number of Total possible events.
You can also say that to find the probability of any given situation or entire population. We need to know about the total possible outcomes of that situation. Only then can we know about the probability of a single event occurring from those situations.
And one of the most important things in Probability is the probability of all the events. That is happening in any situation sums up to 1.
This is one of the most important things to know or to remember whenever you are working on a probability problem or a real-life situation that involves probability of well-defined data to get it solved.
For example, whenever we are going to Toss a Coin, there can be only two outcomes: head (H) or tail (T). There is no chance that both of these outcomes come at one time.
But when we toss 2 coins together in their three possibilities can occur like both the coins can be heads, or both the coins show tails or from both of those coins either one can be head, and another can be tail. That is (H H), (T T), (H T), and (T H). This is how we will get to know about a single event’s probability from the series of events.
What Is The Formula Of Probability?
Now, it is easy to use the formula of probability everywhere, such as to know the birth probability of a larger population. That is defined as the possibility of the occurring element being equal to the ratio of a number of favorable outcomes and the number of Total outcomes.
This means the probability of an event P(E) of a sample size is equal to the number of favorable outcomes divided by the total number of that situation’s outcome.
P(E)= number of favorable outcomes / total number of outcome
Example: There are 10 pillows in a bed; 2 are blue, 5 are yellow, and 3 are red. Calculate the probability of selecting a blue pillow?
The probability of selecting the blue pillow is equal to the number of blue pillows divided by the total number of pillows,
=> 2/10 = 1/5 = 0.20
What Are The Different Types Of Probability?
Now, as we have already discussed, what probability is and its basic formula of the probability. Now it’s time to discuss the types of probability; you read it right. There are three major types of probabilities, and those are:
- Theoretical probability
- Experimental probability
- Axiomatic probability
1. Theoretical probability
Theoretical probability is based on the chances of something happening. We can also say that it is based on the possible chances of things happening in a particular problem, or previous events or a real-life situation. The probability is basically based on the basic reasoning open probability.
|For example, suppose we are tossing a coin, and as we have discussed above, the single coin has only two outcomes either it shows heads or shows tails. So the probability of getting a head or a tail is equal, and that is 0.5 So this was all about one of the most common or basic types of probability i.e., theoretical probability.|
2. Experimental Probability
The name suggests that it is experimental. It means it will consist of some experiments in this type of probability. Basically, we can say that the experimental probability is based on the observation coming from an experiment.
In order to get an answer from such a type of probability, there must be an experiment going on, and from that, we will account or observe the outcomes, and then we will get to know about the probability of any event from that particular experiment.
Note: The experimental probability can be counted as the number of possible outcomes by the number of trials because we are experimenting, and experiments are based on different trials. So the experimental probability will be equal to two possible outcomes by the total number of trials.
|For example, if we toss a coin 10 or 15 times, then the 10 or 15 times are the trials and now how it will get done. Suppose we toss it 10 times and the head is recorded 7 times, then the experimental probability of the head will be 7/10, and the experimental probability of tails will be 3/10.|
3. Axiomatic probability
There is a set of rules in axiomatic probability, or we can call those sets of rules axioms. These rules get applied to all the types of reasons for a set of rules known as Kolmogorov’s three axioms. With the help of axiomatic probability, we can calculate the chances of occurrence and non-occurrence of any event.
And the axiomatic perspective says that probability is any function (we can call it P) from events to numbers satisfying the three conditions (axioms).
And those three conditions are:-
|0 ≤ P(E) ≤ 1 for every allowable event E. (In other words, 0 is the smallest allowable probability and 1 is the largest allowable probability).|
|The certain event has probability 1. (The certain event is the event “some outcome occurs.” For example, in rolling a die, a certain event is “One of 1, 2, 3, 4, 5, 6 comes up.” In considering the stock market, a certain event is “The Dow Jones either goes up or goes down or stays the same.”)|
|The probability of the union of mutually exclusive events is the sum of the individual events’ probabilities. (Two events are called mutually exclusive if they cannot both occur simultaneously). For example, the events “the die comes up 1” and “the die comes up 4” are mutually exclusive, assuming we are talking about the same toss of the same die. The union of events is the event that at least one of the events occurs. For example, if E is the event “a 1 comes up on the die” and F is the event “an even number comes up on the die,” then the union of E and F is the event “the number that comes up on the die is either 1 or even.”|
Formula For The Probability Of An Event
You already know about what probability is and what are the types of probability now you should know about one of the most important formulas. Which is used many times in the branch of probability and regardless of the types of probability this formula is used everywhere.
P(E) = r/n
P(E’) = n-r/n = 1-r/n = 1-P(E)
So, P(E) + P(E’) = 1
This means that the total number or sum of probability can never be more than one.
What Are Equally Likely Events?
When the same theoretical probability of happening, then the probability is known as equally likely events. A sample space results are called equally likely if each event has a similar probability of occurring.
For instance, if a person throws a die, then the probability of occurring 1 is 1/6. Similarly, the probability of occurring all other numbers from 2 to 6, one at the same time, is 1/6.
Let’s test your knowledge about probability!
1. What is the probability that all the events add up in a given sample space?
|Correct Answer: Option 3 (Discussed in section: Some key points about probability!)|
2. A die is thrown. Calculate the probability of obtaining an odd number?
|Correct Answer: Option 4 (Use the formula given in section: What is the formula of Probability?)|
3. The probability that depends on the experiments’ observations is called:
- Theoretical Probability
- Experimental Probability
- Axiomatic Probability
- None of these
|Correct Answer: Option 2 (Details explained given in the section “Experimental Probability”)|
4. The complement of P(E) or P(E’) is:
- None of these
|Correct Answer: Option 1 (Details explained given in the section “Formula for the probability of an event”)|
5. If the numbers of events have the equivalent theoretical probability of occurring, then all are known as:
- Equally likely events
- Mutually exhaustive events
- Mutually exclusive events
- Impossible events
|Correct Answer: Option 1 (Details explained given in the section “What are Equally Likely Events”)|
So, this was all about probability and the different types of probability. We hope that by reading this blog you will get all the essential knowledge needed for working in a branch of probability. If you are a student then this blog must help you with providing important knowledge about probability. So that you can get the most out whenever you study probability and the different types of probability. if you need the assignment of probability, then Get the best probability assignment help from our experts.
Frequently Asked Question
What is the difference between theoretical and experimental probability?
Theoretical probability is about what is supposed to occur or happen. Experimental probability is about the outcome of an experiment.
How many types of events are there in probability?
Types of Events within the probability:
Impossible and Sure Events.
Dependent and Independent Events.
Events Associated with “OR”
Mutually Exclusive Events.
What is an example of an impossible event?
An impossible event is an event, which has the probability of zero and can not happen. E is an impossible event when & only when P(E) = 0. For example, flipping a coin once, there is an impossible event probability of getting BOTH a tail AND a head.