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Classical Probability

However, you could use your intuition to predict some of those probabilities fairly accurately, while others you might have no instinct about at all. What values can the probability of an event take, and what does the value tell us about the likelihood of the event occurring? Many people prefer to express probability in percentages. Since all probabilities are decimals, each can be changed to an equivalent percentage.

Although we will not focus on this type of probability in this course, we will mention a few examples to get you thinking about probability and how it works. A practical use of a coin flip would be for you and your roommate to decide randomly who will go pick up the pizza you ordered for dinner. Many sporting events begin with a coin flip to determine which side of the field or court each team will play on, or which team will have control of the ball first. Each traditional cube-shaped die has six sides, marked in dots with the numbers 1 through 6. Suppose six people go out to dinner.

Randomness, probability, and simulation

You want to randomly decide who will pick up the check and pay for everyone. This particular spinner has three colors, but each color is not equally likely to be the result of a spin, since the portions are not the same size. The red and yellow make up the other half of the spinner and are the same size.

An Introduction To Probability And Statistics For Data Science

Suppose there are 2 freshmen, 1 sophomore, and one junior in a study group. You want to select one person. Suppose we had three students and wished to select one of them randomly. Since we are selecting randomly, each is equally likely to be chosen.


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A single flip of a coin has an uncertain outcome. So, every time a coin is flipped, the outcome of that flip is unknown until the flip occurs.

Introduction to Probability: Probability Formulas, Videos and Examples

However, if you flip a fair coin over and over again, would you expect P H to be exactly 0. The above Learn by Doing activity was our first example of the second way of determining probability: Empirical Observational methods. After doing this experiment, an important question naturally comes to mind. How would we know if the coin was not fair? Certainly, classical probability methods would never be able to answer this question.


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In addition, classical methods could never tell us the actual P H. The only way to answer this question is to perform another experiment. However, their real importance is to answer probability questions that arise when we are faced with a situation that does not follow any pattern and cannot be predetermined. Units require no calculus or matrices; Units require some calculus, no matrices; Unit 7 requires matrices, no calculus. Previous probability or statistics background not required.

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About this course Probability and statistics help to bring logic to a world replete with randomness and uncertainty. This course will give you tools needed to understand data, science, philosophy, engineering, economics, and finance.

You will learn not only how to solve challenging technical problems, but also how you can apply those solutions in everyday life. Meteor showers are rare, but the probability of them occurring can be calculated. Politicians study polls to guess their likelihood of winning an election. Teachers choose a particular course of study based on what they think students can comprehend. Doctors choose the treatments needed for various diseases based on their assessment of likely results.

Lecture 01 Introduction to Probability

You may have visited a casino where people play games chosen because of the belief that the likelihood of winning is good.