probability: discrete vs. continuous

What is the key difference between discrete and continuous probability?

Discrete involves a definite number of possible outcomes; continuous involves an infinite number of possible outcomes.

What is the sample space in discrete probability?

It’s the set of all possible outcomes.

How do you calculate a discrete probability?

Divide the number of favorable outcomes by the total number of possible outcomes.

What is the gambler’s fallacy?

Where a person essentially mistakes independent events for dependent events. (e.g., thinking tails is "due" after many heads).

What are dependent vs. independent events?

Dependent events are those where the outcome of one instance affects the outcome of a subsequent instance; independent events are those where probability is unchanged from instance to instance.

What’s the difference between non-exclusive and mutually exclusive outcomes?

Non-exclusive outcomes are those that can occur simultaneously; mutually exclusive outcomes where none of the possibilities can occur simultaneously.

What are the rules for AND/OR in probability?

Use multiplication for AND; use addition for OR.

What are probability distributions?

Tells us which values are most/least probable for the variable we’re studying.

• There are discrete probability distributions (which can be characterized with probability mass functions and analyzed using combinatorics) and continuous probability distributions (which can be characterized with probability density functions and analyzed using calculus)

What is the cumulative distribution function (CDF)?

Starts with our lowest data value and increases to our highest data value. It tells us the probability of getting a value lower than the one we’re looking at. The CDF shows us how quickly/slowly we increase from 0% to 100%.