Mean (expected value) of a discrete random variable

Definition Of Outcome. A possible result of a probability experiment is called an outcome. Examples of Outcome. Head is a possible outcome when a coin is tossed. 6 is a possible outcome when a number cube is rolled. Video Examples: Probability of More Complex Outcome. Probability model: Tells what possible outcomes and assigns probability to these outcomes-We can find the probability of any collection of outcomes by summing them up-Sometimes collection of outcomes is called an “event” Probability rules: A. Any probability is a number between 0 and 1: Any proportion is between 0 and 1, so any probability is also a number between 0 and 1.

Sign up or log in to Magoosh Statistics. You probably wonder how predicted probability is different from normal probability. Well, it has to do with how the probability is calculated and what the outcomes mean. Well, a predicted probability is, essentially, in its most basic form, the probability of an what is the meaning of endow that is calculated from available data.

In the initial stages of predicting probability, you use the simple probabilities of a few events occurring in some combination. What is the probability of rolling two consecutive sixes using a fair die? In this case, we use the fact that rolling a fair die is a mutually exclusive event. The probability of *what does outcome mean in probability* a single six is 0. Therefore, the probability of rolling two sixes is the product of the individual probabilities. The calculations for dependent events are similar to those for mutually exclusive events.

Of course, we have to consider how one event affects the next. What is the probability of drawing two from a standard deck of cards without replacement? First, the probability of drawing the first queen is. But the probability of drawing a second queen is different because now **what does outcome mean in probability** are only three queens and 51 cards.

So far, we have discussed the probability of single events occurring. However, what if you wanted to figure out the probability of more complex complementary events occurring? For example, the probability of dropping out of school based on sociodemographic information, attendance, and achievement.

In this case, we have several indicators and complementary events. One way that we calculate the predicted probability of such binary events drop out or not drop out is using logistic regression. Unlike regular regressionthe outcome calculates the predicted probability of mutually exclusive event occuring based on multiple external factors. You may notice that logistic regressions involve the regression coefficients as a superscript to the value of e.

This means that the coefficients have an effect on the probability. As an effect on probability, the coefficients represent odds instead of simple numerical relationships.

The fact that the coefficients represent odds ratios is particularly useful in light of the fact that the logistic regression predicts probabilities instead of a how to stop itching hands and feet outcome. Predicted probabilities are fairly straightforward. They are probabilities that are calculated from existing probabilities, though the method does depend on the nature of the probabilities involved. For example, mutually exclusive and complementary events predict probability as the product of event probabilities, the probability of dependent and complementary events has to be calculated as a sequence.

Furthermore, logistic regression is a method of predicting probabilities based on more complex variable interaction, although the regression equation itself represents odds instead of traditional slope relationships.

Magoosh blog comment policy : To create the best experience for our readers, we will only approve comments that are relevant to the article, general how to connect rg59 cable to bnc connector to be helpful to other students, concise, and well-written!

We highly encourage students to help each other out and respond how to use a mitre box **what does outcome mean in probability** students' comments if you can! If you are a Premium Magoosh student and would like more personalized service from our instructors, you can use the Help tab on the Magoosh dashboard. By John Clark on April 12, in Probability.

The Terminology of Probability

Thus, if we want to calculate the probability of drawing an ace from a standard deck of playing cards, we can divide the number of outcomes in the event where an ace is drawn (4) by the total number of possible outcomes where any card is drawn (52). The probability is then 1/ The probability of any outcome is the long-term relative frequency of that outcome. Probabilities are between zero and one, inclusive (that is, zero and one and all numbers between these values). P P (A A) = 0 0 means the event A A can never happen. P P (A A) = 1 1 means the event A A always happens.

Probability is a measure that is associated with how certain we are of outcomes of a particular experiment or activity. An experiment is a planned operation carried out under controlled conditions. If the result is not predetermined, then the experiment is said to be a chance experiment. Flipping one fair coin twice is an example of an experiment.

A result of an experiment is called an outcome. The sample space of an experiment is the set of all possible outcomes. Three ways to represent a sample space are: to list the possible outcomes, to create a tree diagram, or to create a Venn diagram. An event is any combination of outcomes. The probability of any outcome is the long-term relative frequency of that outcome. Probabilities are between zero and one, inclusive that is, zero and one and all numbers between these values. Equally likely means that each outcome of an experiment occurs with equal probability.

The sample space has four outcomes. This important characteristic of probability experiments is known as the law of large numbers which states that as the number of repetitions of an experiment is increased, the relative frequency obtained in the experiment tends to become closer and closer to the theoretical probability.

Even though the outcomes do not happen according to any set pattern or order, overall, the long-term observed relative frequency will approach the theoretical probability.

The word empirical is often used instead of the word observed. It is important to realize that in many situations, the outcomes are not equally likely. A coin or die may be unfair , or biased. The data seem to show that the coin is not a fair coin; more repetitions would be helpful to draw a more accurate conclusion about such bias. Some dice may be biased. Look at the dice in a game you have at home; the spots on each face are usually small holes carved out and then painted to make the spots visible.

Your dice may or may not be biased; it is possible that the outcomes may be affected by the slight weight differences due to the different numbers of holes in the faces. Gambling casinos make a lot of money depending on outcomes from rolling dice, so casino dice are made differently to eliminate bias.

Casino dice have flat faces; the holes are completely filled with paint having the same density as the material that the dice are made out of so that each face is equally likely to occur. Later we will learn techniques to use to work with probabilities for events that are not equally likely. A conditional reduces the sample space. For example, suppose we toss one fair, six-sided die.

It is important to read each problem carefully to think about and understand what the events are. Understanding the wording is the first very important step in solving probability problems. Reread the problem several times if necessary. Clearly identify the event of interest. Determine whether there is a condition stated in the wording that would indicate that the probability is conditional; carefully identify the condition, if any.

A fair, six-sided die is rolled. Compute the following probabilities:. In this module we learned the basic terminology of probability. The set of all possible outcomes of an experiment is called the sample space. Events are subsets of the sample space, and they are assigned a probability that is a number between zero and one, inclusive.

Skip to main content. Module 3: Probability. Search for:. Example A fair, six-sided die is rolled. Licenses and Attributions. CC licensed content, Shared previously.

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