Cheat Sheet

Probability For Dummies

From Probability For Dummies by Deborah J. Rumsey, PhD

Successfully working your way through probability problems means understanding some basic rules of probability along with discrete and continuous probability distributions. Use some helpful study tips so you're well-prepared to take a probability exam.

Principles of Probability

The mathematics field of probability has its own rules, definitions, and laws, which you can use to find the probability of outcomes, events, or combinations of outcomes and events. To determine probability, you need to add or subtract, multiply or divide the probabilities of the original outcomes and events. You use some combinations so often that they have their own rules and formulas. The better you understand the ideas behind the formulas, the more likely it is that you'll remember them and be able to use them successfully.

Probability rules


Probability definitions


Probability laws


Counting rules


Discrete Probability Distributions

In probability, a discrete distribution has either a finite or a countably infinite number of possible values. That means you can enumerate or make a listing of all possible values, such as 1, 2, 3, 4, 5, 6 or 1, 2, 3, . . .

There are several kinds of discrete probability distributions, including discrete uniform, binomial, Poisson, geometric, negative binomial, and hypergeometric.


Continuous Probability Distributions




Probability Study Tips


  • The relationship between mutually exclusive and independent events

  • Identifying when a probability is a conditional probability in a word problem

  • Probability concepts that go against your intuition

  • Marginal, conditional, and joint probabilities for a two-way table

  • The Central Limit Theorem:

  • When to use a permutation and when to use a combination

  • Finding E(X) from scratch and interpreting it

  • Sampling with replacement versus without replacement

  • The Law of Total Probability and Bayes' Theorem

  • When the Poisson and exponential are needed in the same problem

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