Basic Statistics and Data Analysis

Lecture notes, MCQS of Statistics

Classical Probability: Example, Definition, and Uses in Life

Classical probability is the statistical concept that measures the likelihood (probability) of something happening. In a classic sense, it means that every statistical experiment will contain elements that are equally likely to happen (equal chances of occurrence of something). Therefore, the concept of classical probability is the simplest form of probability that has equal odds of something happening.

Classical Probability Examples

Example 1: The typical example of classical probability would be rolling of a fair dice because it is equally probable that top face of die will be any of the 6 numbers on the die: 1, 2, 3, 4, 5, or 6.

Example 2: Another example of classical probability would be tossing an unbiased coin. There is an equal probability that your toss will yield either head or tail.

Example 3: In selecting bingo balls, each numbered ball has an equal chance of being chosen.

Example 4: Guessing a multiple choice quiz (MCQs) test with (say) four possible answers A, B, C or D. Each option (choice) has the same odds (equal chances) of being picked (assuming you pick randomly and do not follow any pattern).

Formula for Classical Probability

The probability of a simple event happening is the number of times the event can happen, divided by the number of possible events (outcomes).

Mathematically $P(A) = \frac{f}{N}$,

where, $P(A)$ means “probability of event A” (event $A$ is whatever event you are looking for, like winning the lottery, that is event of interest), $f$ is the frequency, or number of possible times the event could happen and $N$ is the number of times the event could happen.

For example,  the odds of rolling a 2 on a fair die are one out of 6, (1/6). In other words, one possible outcome (there is only one way to roll a 1 on a fair die) divided by the number of possible outcomes.

Classical probability can be used for very basic events, like rolling a dice and tossing a coin, it can also be used when occurrence of all events is equally likely. Choosing a card from a standard deck of cards gives you a 1/52 chance of getting a particular card, no matter what card you choose. On the other hand, figuring out will it rain tomorrow or not isn’t something you can figure out with this basic type of probability. There might be a 15% chance of rain (and therefore, an 85% chance of it not raining).

Other Examples of classical Probability

There are many other examples of classical probability problems besides rolling dice. These examples include flipping coins, drawing cards from a deck, guessing on a multiple choice test, selecting jellybeans from a bag, and choosing people for a committee, etc.

Classical Probability cannot be used:

Dividing the number of events by the number of possible events is very simplistic, and it isn’t suited to finding probabilities for a lot of situations. For example, natural events like weights, heights, and test scores need normal distribution probability charts to calculate probabilities. In fact, most “real life” things aren’t simple events like coins, cards, or dice. You’ll need something more complicated than classical probability theory to solve them.

For further Detail see Introduction to Probability

The Author

Muhammad Imdadullah

Student and Instructor of Statistics and business mathematics. Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan. Like Applied Statistics and Mathematics and Statistical Computing. Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis etc.

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