Mathematics is often regarded as a difficult subject, but it is equally engaging when compared to other subjects. Mathematics also has its share of ups and downs, good and bad. There are some chapters and topics that students enjoy, and then there are chapters that students don’t wish to study. One such topic is empirical probability. You must have heard of it, right? At least you would have heard of probability. So the empirical probability is a topic that falls in the same chapter. You must have solved questions wherein you get a dice or a pack of cards or a coin to toss. In these questions, you have to assume a few things and then figure out the results. At times probability questions can be tricky and time-consuming, but you need to have a grip on the tricks and tips to solve them.
In this article, we are going to talk about everything related to this topic. We will also be discussing the tricks and tips that can help you in solving these questions easily.
What Is Probability?
To define what’s probability in the best way possible, we need to assume things. Have you ever wondered about a situation or an event occurrence? If yes, then that’s probability. If there is an event that’s going to happen, as it may rain or not. Here the probability of the event happening will be 50-50, which means the probability is ½. Things like these that are not certain have a probability parameter that decides the outcome of any event. Talking theoretically, probability can be in percentage, decimal, or even infractions.
Another thing to keep in mind while studying probability is that it can be anywhere between 0-1. If any event has a probability of 0, it indicates that the probability of that event happening will be 0. Something between 0-1 will be a probability, and if the result comes out to be 1, it means that the event is a sure event.
What Is Empirical Probability?
Empirical Probability is defined as the experimental probability of an event that is based on the results of a certain experiment conducted several times. In a theoretical probability, generally, the outcome is determined based on the prediction of an event. Whereas empirical probability is determined with the help of actual experiments and previous recordings of any particular event. As the name suggests, the experimental or empirical probability is equal to the proportion of the number of events that occurred to the total number of trials.
More Insights on Empirical Probability
Empirical Probability is trusted by people because it is not based on luck or anticipation. The results you get in empirical probability depend only on experimental studies and concrete data. The results that you get in this are free from any hypothesis or assumptions. But on the flip side, you can have a few setbacks that show that blindly trusting empirical outcomes can also be problematic. Here are two flip sides of empirical probability:
- Incorrect conclusion
If you look closely at the theory and results of the empirical formula, you will be able to understand that there is a flaw in it. Assume that there is a coin that’s been tossed by a person three times. He luckily got three heads. In this case for him, the data when someone asks will be “call for the head when the coin is tossed.” But it is not fixed that when the coin is tossed for the fourth time, the result will be a head. So this turns out to be a flaw in the theory. As we have already discussed that empirical probability is based on results and previous data, which is why it is free from assumption. But in the example discussed above, we can clearly see that if we use the empirical formula here, there can be a problem and we will not get the right answer.
- Is the sample size sufficient?
The second thing that makes the results and theory of empirical probability a bit problematic is the insufficient sample size. It is a fact that can’t be changed. If you wish to determine accurate answers, you need to have bigger or larger sample sizes. Smaller or lesser samples will result in inaccurate answers. Therefore to display a good representation of empirical probability, you need to have a larger or bigger sample size.
Here’s a perfect example to make you understand this point. Assume that you have a coin. You toss it up twice. Now the probability of getting heads can be 0%, 100% or 50-50. Now with such a small sample size, you won’t be able to take out the probability result convincingly.
This is the reason why there are different probabilities for different sample sizes, and each one of them has significance.
Different Types of Probabilities
The next thing to understand here is the types of probability. This is a cap topic, and a lot of types come under this. Empirical Probability is one of the types of probabilities that is taught to the students. Here are some of them.
- Classical probability
Classical probability is widely known as theoretical probability, and it is highly based on formal reasoning. Generally, this topic is covered in every course, and you have to solve problems related to this. In classical probability, if a coin is tossed the probability of getting heads or tails is going to be 50-50.
- Subjective probability
Now, as the name suggests, a subjective probability refers to the results or probability based on someone’s experience or personal judgment. If there is a restaurant where 3 of your friends might have gone for dinner. They had the same meal. You ask them all about their feedback. You cannot assume that all of them will give positive feedback. So these cases are called as subjective probabilities. Every individual is going to have a different result.
How to Distinguish Empirical Probability from Calculated Probability?
There is a hairline difference between empirical probability and calculated probability. Where the empirical probability is an estimated outcome, the calculated probability involves the distinct outcomes of an exact space.
Things to Keep in Mind While Solving a Question of Probability
- One of the most confusing things about probability is the use of “and/or.” If you want to score good marks in your exams, make sure that you learn the difference between “and/or.”
- Similarly, many students face problems in “mutually exclusive” and “independent events.” Both these things are completely different, and right from approaching these questions to solving them, there are different steps that you need to follow.
- At times students get confused in solving the independent random variable problems. All you need to understand in these questions is that the two variables given in the question are completely different and have no correlation between them.
- Half your question is solved when you start visualizing your problems. Like many other chapters and topics, probability is also one topic where you need to visualize your question first. Trigonometry, statistics, and volume questions are a few other topics that need the same treatment. If you visualize a question before solving it, you can easily solve it because you have the graphics of that question in your head. Visualization is also important because it helps in applying logic easily to the problems you have in front of you.
- One of the best ways to solve these questions is to apply various theorems. True, you have a lot of them, but the person who knows the application of these theorems can easily use it and solve the questions easily. Also, there are some situations, or we can say conditions where you will have to apply theorems to solve the questions.
- Probability is all about conditions and situations. So, you should always expect a problem to have conditions. Make sure that you have practiced these enough times. They usually restrict students from performing well. Make sure you are not one of them.
- Mostly you are going to get cards, dice and multiple coins. In situations like these, you should always consider writing all the possible cases or outcomes. This will help you in not missing out any possible option. You will never get an answer wrong if you make yourself perfect in this trick. Also, many people do follow this even when they are doing their higher studies.
Understanding various probabilities and their applications can be a bit tricky at times. While studying this topic, you need to keep in mind that there is a marginal difference between them. You will have to practice all of them to get an understanding. Learn Data about the types of probability and make sure that you are well-versed with all of them.
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