Muddy Points

Fall 2025

1. I think I get the general concepts. However, when it comes to questions, what keywords am I looking for when applying each theorem. Like if question is asking about a specific probability, what theorem?

When trying to figure out what theorem/rule/property to use, the most helpful thing is to (1) write the probability statement for your answer and (2) write the information you know in probability statements. Then you want to examine all the rules/theorems/properties we learned to see which can help you connect the information you know to the probability statement for the question.

Fall 2024

1. How do I know if two events are independent?

My main piece of advice for independence is to rely on the math to show it, not logic! Don’t go into a problem thinking “Logically, these two events are independent.” If the problem does not say “Assume independence,” then we need to show it mathematically.

Same goes with the definition of independence. When we say “knowing the outcome of one provides no information about the outcome of the other,” we once again need to show this mathematically, not just using logic. We translate the previous statement to \[P(A) = P(A|B)\] And we need to show this mathematically!

2. Disjoint vs. Independent Events

Here is a pretty good video breaking down disjoint (mutually exclusive) events and independent events. It includes examples as well.