Key Concepts

Review core concepts you need to learn to master this subject

Union

The union of two sets encompasses any element that exists in either one or both of them. We can represent this visually as a venn diagram as shown. Union is often represented as:

(A or B)(A\ or\ B)
Rules of Probability
Lesson 1 of 1
  1. 1
    Probability is a way to quantify uncertainty. When we flip a fair coin, we say that there is a 50 percent chance (probability = 0.5) of it coming up tails. This means that if we flip INFINITELY man…
  2. 2
    Let’s dive into some key concepts we will use throughout this lesson: union, intersection, and complement. #### Union The union of two sets encompasses any element that exists in either …
  3. 3
    Imagine that we flip a fair coin 5 times and get 5 heads in a row. Does this affect the probability of getting heads on the next flip? Even though we may feel like it’s time to see “tails”, it is i…
  4. 4
    Two events are considered mutually exclusive if they cannot occur at the same time. For example, consider a single coin flip: the events “tails” and “heads” are mutually exclusive because we cann…
  5. 5
    Now, it’s time to apply these concepts to calculate probabilities. Let’s go back to one of our first examples: event A is rolling an odd number on a six-sided die and event B is rolling a num…
  6. 6
    If we want to calculate the probability that a pair of dependent events both occur, we need to define conditional probability. Using a bag of marbles as an example, let’s remind ourselves of the de…
  7. 7
    We have looked at the addition rule, which describes the probability one event OR another event (or both) occurs. What if we want to calculate the probability that two events happen simultaneously?…
  8. 8
    We have introduced conditional probability as a part of the multiplication rule for dependent events. However, let’s go a bit more in-depth with it as it is a powerful probability tool that has rea…
  9. 9
    Imagine that you are a patient who has recently tested positive for strep throat. You may want to know the probability that you HAVE strep throat, given that you tested positive: P(ST \mid +) T…
  10. 10
    Congratulations, we have finished our exploration into the rules of probability! To recap, we have covered: * The union and intersection of two events * The complement of an event * Independent an…

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