Third, if two events A and B are mutually exclusive, then the probability of the union of these events is the sum of the probabilities of each event individually. That is,. If the events are not mutually exclusive that is, they share some elements in common , then the probability of their union is sum of the individual probabilities minus the probability of all elements in common this is just the intersection of A and B.
This formula is actually a more general expression of the preceding formula. Fourth and finally, the probability of an event E is equal to unity minus the probability of the event's complement, E C. This statement simply combines the facts that E and E C are mutually exclusive but span the entire sample space S and that the probability of S is unity.
Thus, using the rules above,. Although these rules and concepts may seem somewhat esoteric, they are indeed helpful in discussing probability as it relates to statistics. The following practice problems will help you apply these ideas to practical problems and situations. Practice Problem : For a random experiment involving the roll of a sided die, what is the probability that the outcome will be between 1 and 10 inclusive?
Because the event for which the outcome of a roll is between 1 and 10 inclusive spans the sample space, the probability must simply be unity. Practice Problem : Given a standard deck of 52 playing cards, what is the probability that a card pulled from the deck is either an ace or a spade? Solution : This problem forces you to apply several different aspects of statistics. The problem defines two events, which we will call A and P. Event A is the selection of an ace, and event P is the selection of a spade.
Although you may realize already that A and P are not mutually exclusive events, let's write out the two sets to illustrate. The notation used below is the value of the card A for ace, for example followed by the suit of the card S for spades, for example.
Note that one element outcome is shared between the two sets. Let's now write the probability formula for the union of A and P , which is the probability that the card selected is either a spade or an ace. Now, we must calculate these probabilities. Let's use these numbers to calculate the probability that a random drawing of a card yields either an ace or a spade:.
Of course, a simpler approach would simply be to find the relative frequency of aces and spades there are 16 such cards in a deck --again, this is just 0.
The solution above, however, illustrates the use of the concepts presented in this article. Other problems may not always be as easily solved.
Open Main Menu. Browse Courses My Classes. Sign In Subscribe Course Catalog. What is Probability in Statistics? Probability Theory Because data used in statistical analyses often involves some amount of "chance" or random variation, understanding probability helps us to understand statistics and how to apply it.
Key Terms o Random experiment o Outcome o Event o Sample space o Mutually exclusive o Random variable o Probability o Complement o Union o Intersection Objectives o Recognize and understand the basic terms associated with probability theory o Learn how probability is related to statistics o Perform simple calculations related to probability Probability and statistics are actually quite extensively linked.
Probability Terms Although the concept of randomness or chance is difficult to define, we will simply assume that an experiment or observation whose outcome cannot be predicted is a random experiment. Second, we can refer to the union of two events A and B using the following notation: The union is simply the set of all outcomes contained in either A or B or both. As a result of the comprehensive model developed, the behaviour of the individual elements can be predicted.
But in statistics, a small number of observations is used to predict the behaviour of a larger set whereas, in probability, limited observations are selected at random from the population the larger set. The probability model provides the data regarding the population. Coming from Engineering cum Human Resource Development background, has over 10 years experience in content developmet and management. A more practical question would be to ask what differences exist between the work of contemporary statisticians and contemporary probabilists.
The answer to that is that yes, statisticians are concerned primarily with describing data. They use either parametric models based upon mathematical probability distiributions or non-parametric approaches based upon empirical distributions harder.
Their interests center on bias, precision and reproducibility. Modern probabilists have moved on from mathematical statistics.
One active area is concerned primarily verifying probabilistic conjectures in physics. Most notably, probabilists are concerned with proving limit theorems, finding bounds in the limit for distributions arising in complex systems and the like.
Therefore the true Logic for this world is the Calculus of Probabilities, which takes account of the magnitude of the probability which is, or which ought to be in a reasonable man's mind. For example, if we make a complete census of the entire population of a nation and count the exact number of people belonging to particular groups such as age, gender, and so on, we are doing statistics.
There's no uncertainty — probability — involved, because the numbers we find are exact and known. On the other hand, imagine someone passing in front of us on the street, and we wonder about their age. In this case we're uncertain and we use probability, but there is no statistics involved, since we aren't making some sort of census or catalogue. But the two can also occur together. If we can't make a complete census of a population, we have to guess how many people are in specific age-gender groups.
Hence we're using probability while doing statistics. Vice versa, we can consider exact statistical data about people's ages, and from such data try to make a better guess about the person passing in front of us. Hence we're using statistics while deciding upon a probability. Sign up to join this community.
The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. What's the difference between probability and statistics? Ask Question. Asked 11 years, 3 months ago. Active 8 months ago. Viewed 96k times. Improve this question. Dmitrij Celov 5, 2 2 gold badges 27 27 silver badges 41 41 bronze badges.
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Perhaps it's interesting to mention that if one thinks that the plausible inductive reasoning should be consistent, then actually the result is bayesian statistics, and more interesting this can be derived from probability theory. So bayesian statistics is basically applied probability theory so to speak.
Show 1 more comment. John D. Cook John D. Cook 3, 1 1 gold badge 24 24 silver badges 27 27 bronze badges. A probabilist might ask "given I've drawn three red beans, what is the probability that the proportion is fifty fifty? Ben Cann 3 5 5 bronze badges. Harvey Motulsky Harvey Motulsky Justin Bozonier Justin Bozonier 1, 2 2 gold badges 10 10 silver badges 23 23 bronze badges. Some examples follow: Quantifying Uncertainty Example 1: You roll a 6-sided die.
What is the probability of obtaining a 1? Explaining Variation Example 1: We observe that the annual income of a person varies. Alexis You can only get a statistic from a sample, otherwise if you compute a numerical measure on a population, it is called a population parameter. Tony Breyal Tony Breyal 3, 1 1 gold badge 17 17 silver badges 13 13 bronze badges. You intuitively know what probability is.
Carlos Accioly Carlos Accioly 4, 4 4 gold badges 25 25 silver badges 27 27 bronze badges. A description of the mathematical theory can give us a small idea of what a subject is about, but it is not the subject itself.
Statistics is "more subjective" and "more art than science" relative to probability. Different statisticians will give different, often long-winded answers. TheodoreM TheodoreM 31 1 1 bronze badge. But in trying to be more helpful, practical with an answer Commonly it has helped me to see things such as There's inductive and deductive Statistics, so that's not where the difference lies. Community Bot 1. Hirak Mondal Hirak Mondal 1.
Let me quote the relevant passage: When the working members of Section F get hold of a Report of the Census, or any other document containing the numerical data of Economic and Social Science, they begin by distributing the whole population into groups, according to age, income-tax, education, religious belief, or criminal convictions. So we can say: — In statistics we are "concentrating our attention on small number of artificial groups" or quantities; we're making a sort of cataloguing or census.
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