Content
What is probability
Probability is a branch of mathematics described as mutually exclusive events that we frequently experience in our daily lives, knowingly or unknowingly. What are the odds that it will rain? How likely is it to win the lottery? Even if we can’t always forecast these things, knowing the precise probability of an event might help us make wise decisions. In other words, probability determines the occurrence of events or how likely they can occur.
Let us discover how to learn probability.
Looking to Learn Probability? Book a Free Trial Lesson and match with top Probability Tutors for Concepts, Homework Help, and Test Prep.
Basics of Probability
The basics of probability consist of basic terms you must know to start your learning journey. They are:
- Randon Experiment: A random experiment is a process where you can repeat the event over and over again. In this recurring experiment, you cannot predict the outcome with certainty. Each time you repeat the experiment, it is called a trial.
- Outcomes: These are the results of a random experiment. You can only receive one outcome at a time.
- Sample Space: This is an amalgamation of all the possible outcomes. It is usually denoted as a sample space. It is represented with curly brackets, {}.
- Favorable Outcome: These are outcomes in the sample space that you want to pick out to calculate a probability for. For example, there are six different outcomes. What’s the probability of rolling a one? (Favourable outcome is one).
- Event: An event is a part of a sample space to which you can assign a probability. They are also represented with a curly bracket {} and delivered from a probability formula.
- Chance: Chance is often used as probability, itself. You can use either of them interchangeably.
- Odds: Odds and probability are related terms but not the same. Odds are calculated based on ratios of two probabilities.
Types of Probabilities
Theoretical probability
It is based on the possible chances of something to happen. Theoretical probability can be applied to a wide range of problems. It cannot be used in cases where the number of favorable outcomes is not all equally likely outcomes. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.
Experimental probability
It is based on the observations of an experiment. It can be calculated depending on the possible number of favorable outcomes by the total number of possible trials. For example, if a coin is tossed 10 times and the head is recorded 6 times then, the experimental probability for heads is 6/10 or, 3/5.
Axiomatic Probability
A series of rules by Kolmogorov’s three axioms apply to all the other types. With the axiomatic approach to probability, the chances of occurrence or non-occurrence of the events can be quantified. These three axioms represent that
For any event A, the probability of A is always 0 or more. This means the chance of event A happening is never negative and is always a non-negative number.
When you calculate probability of any outcome, the chance of getting an outcome is one hundred percent.
If A and B are mutually exclusive outcomes, the probability of either A or B happening is the math probability of A happening plus the probability of B happening.
Classical Probability
Classical probability refers to the approach based on assuming that experiments have a fixed number of possible outcomes, which are equally likely outcomes. The probability of an event is the ratio of favorable outcomes to the total event occurring.
For example, the probability of drawing a black card is 26/52 =5 from a deck of cards. If you assume that each of the 52 cards in the deck has an equal chance of being chosen.
How to learn probability: 3 best resources
#1 Probability tutoring services
Wiingy
Wiingy offers 1-on-1 sessions with verified and experienced probability tutors. Every tutor undergoes a rigorous vetting process, including interviews and several tests, with less than 3% of applicants qualifying to teach on the Wiingy platform. The tutors will guide you through solving complex probability problems with step-by-step solutions, addressing your specific needs in the subject.
They cover core probability concepts comprehensively, offering personalized lessons, homework help, and test preparation at an affordable rate, with lessons starting at just $28/hr.
Wyzant
Wyzant is an online tutoring service that offers 1-on-1 lessons in an interactive digital classroom with live video chat for direct communication. To get started with online probability tutoring with Wyzant, you need to answer a few questions about your tutoring needs, and the platform will provide a list of suitable tutors, personalized for you.
You are assured of a “Good Fit Guarantee” with your tutor. If you are not satisfied with your probability tutor in your 1st hour, then you are not committed to paying for that lesson without questions asked. The price ranges from as low as $10 to as high as $600 per hour for each lesson. According to Wyzant, the average tutor cost is around $35 to $65 per hour.
Learner
Learner offers customized tutoring sessions, making sure that every student’s particular requirements and learning pattern are met. Their tutors are very skilled and knowledgeable in teaching probability, and they can efficiently break down difficult concepts and terms.
Learners keep track of students’ development, giving regular feedback and modifying instruction to guarantee ongoing advancement. This method ensures that important probability concepts, such as understanding sample space and deriving formulas, are taught in a way that enhances the learner’s critical thinking and logical decision-making skills in probability.
#2 Probability online courses
Probability and Stats — University of London
The University of London offers an engaging course on combined learning of statistics and probability tailored for all types of learners. This course is 10 weeks long, and you will have the opportunity to watch informative videos, complete tests, and chat with peers. This practice has helped students to enhance their learning experience.
With just a basic understanding of math as a prerequisite, this course is accessible to a wide audience, making it an excellent option for those looking to strengthen their statistical knowledge. London University is renowned for its high-quality academics, thus, it creates a supportive learning community through its courses. You are also eligible to be awarded a certificate from the university once you complete the course.
Udacity
Udacity is an education technology platform associated with Accenture. It uses Accenture’s AI-powered support to help students with a variety of courses.
Intro to Statistics is a course that provides deeply focused information on probability as well. courses provide real-world projects that go far beyond step-by-step guides. They aim to develop critical thinking for workplace relevance.
Udacity’s expert educators enable learning with personalized support and teaching patterns and verify complete mastery of the necessary statistical skills.
Coursera
Coursera is another prominent course platform that collaborates with prestigious academic institutions like Yale University, and the University of Michigan. It also associates with top-notch corporations like Google, Goldman Sachs, and others to provide well-structured and legitimate information on statistics.
There are courses for combined learning of probability and statistics. Duke University’s course named, “Introduction to Probability and Data with R” gives a step-by-step process to learn probability, well suited for beginners. This course is 14 hours approx. with flexible timing, hence you can learn at your own pace.
#3 Probability worksheets
Common Core sheets
Common Core Sheets provides free printable math worksheets or interactive resources with a diverse range of educational materials designed to accommodate different learning needs and preferences.
It is made especially to match Common Core State Standards, guaranteeing that the content is appropriate and covers the ideas and abilities. It fulfills all your probability example, sample, and practice needs.
Math Aids.com
It offers tutors, parents, students, and homeschoolers free probability worksheets. You can select different variables to customize the worksheets as per your preference. These are free to download, printable, and easy to use.
Math Aids.com uploads its probability worksheets every day. Therefore, it has endless provision of new worksheets. These probability worksheets are helpful for children in grades 5, 6, 7, and 8. These focus mainly on selected questions that generally come for exams, they aim at recreating similar questions in abundance.
Super Teacher Worksheets
It offers math worksheets for high school students, including probability, statistics, and geometry. The site provides resources for teachers, parents, and homeschoolers. The worksheets are designed by educators, ensuring alignment with academic standards. Each sheet provides clear instructions and relevant practice problems.
These worksheets are categorized under each function of probability. For example, heads and tails, samples, cards, pebbles, and more.
How to Understand Probability
You use probability in your everyday life, even if you don’t realize it. It’s similar to making daily decisions without considering the repercussions or possibilities. Some of the real-world examples of probability are:
Weather: the meteorologists cannot determine the exact change of events in the weather. Thus, they use tools to predict the probability of snow or rain. For example, there is a 40% chance of rain, which means it has rained on 40 out of 100 days with similar weather conditions.
Sports/Games: Coaches and athletes frequently use probability to figure out the best sports strategies for competitions and games. For example, if a football player scores 10 out of 15 field goals throughout the season, the probability of him scoring his next field goal is 10/15 or 2/3.
Another example is in a board game or a card game, you often seek for the odds of a desirable outcome. The probability of that one favorable event to happen helps you to determine when to take a risk or how much risk you should take.
Why Learn Probability
To make wise decisions in a variety of domains, including science, engineering, finance, and daily life, one must have a solid understanding of probability. To improve forecasts and risk assessments, it aids in the comprehension and measurement of uncertainty.
When data analysis, model creation, and prediction are considered then, probability theory is essential in domains such as statistics, data science, and artificial intelligence. Furthermore, it strengthens your critical thinking and problem-solving capacity, enabling you to approach complicated circumstances with reason and method.
One can make better judgments in both their personal and professional life with a solid understanding of probability.
Looking to Learn Probability? Book a Free Trial Lesson and match with top Probability Tutors for Concepts, Homework Help, and Test Prep.
Conclusion
In conclusion, learning probability is a valuable skill that opens doors to numerous opportunities in various fields. To enhance your learning experience, consider utilizing diverse resources such as probability tutoring services, which offer personalized guidance and support. Online courses provide structured learning paths and interactive content to deepen your understanding.
Additionally, practice worksheets are excellent tools for reinforcing concepts and honing your problem-solving skills. With these resources, you can confidently embark on your journey to mastering probability and unlock its full potential.
Other useful resources
FAQs on How to learn Probability
How can I be good at probability?
You can be good at probability by first having a basic understanding of the terms used in the topic. If you practice regularly with different types of questions and with real-world examples, you can improve your skills in probability.
You can use worksheets, textbooks, and online resources to further work on your probability skills.
How can I learn probability easily?
Easy ways to learn probability are to build your foundation, understand basic principles, and use interactive tools like flowcharts, Venn diagrams, and more.
Tutoring services, both online and offline, can provide personalized guidance and clarify doubts, in addition. Platforms like Wiingy offer probability tutoring best suited for your needs.
Is it hard to learn probability?
While probability can be challenging, it is not unachievable. With the right mindset, resources, and support, you can successfully learn and master probability.
How to learn probability quickly?
To learn probability quickly, start by focusing on the core concepts such as basic rules of probability, conditional probability, and probability distributions.
Engage yourself in tutorials, courses provide by Khan Academy and Udemy. Seek personalized help from tutoring services like Wiingy and Wyzant to address specific questions and accelerate your understanding.
Written by by
Medha PandeyReviewed by by
Prerit JainShare article on
