What is an experiment?
An activity or process that is infinitely repeatable yielding the same set of results every time (coin flip, dice roll, ect.)
What is an outcome?
The result of an experiment
What is the Sample Space?
The collection of all possible outcomes of an experiment
What is an event?
Any set of outcomes that are a subset of the sample space within an experiment
Definition of the fundamental principle of counting
In an experiment with k steps, the total number of outcomes is the number of choices to the power of the number of steps.
What are Permutations?
(do they account for order or not?)
The number of ways to arrange r objects from n objects.
Order IS accounted for, therefore, AB and BA are different entries. (every entry is unique)
EX: # Ways to arrange 5 teachers from a group of 8 teachers
What are combinations?
(do they account for order or not?)
The number of combinations of r objects taken from n distinct objects. Denoted by nCr.
Combinations DO NOT account for order, therefore, AB and BA are the same result.
How do we define the probability of an event?
The proportion of times an outcome occurs after repeating the experiment infinite times
What is theoretical probability?
It is another name for the probability of an event
What is empirical probability?
Finding the probability of an event, E, by repeating an experiment many times.
What is the law of large numbers?
The idea that by doing more repetitions of an experiment, the relative frequency of obtaining result E comes closer to the theoretical probability (More trials -> greater accuracy)
What does it mean if two outcomes are “mutually exclusive?” (What is another word for this?)
If those two outcomes cannot occur at the same time.
The two outcomes are DISJOINT.
Define the probability of complements.
The set of all possible outcomes that ARE NOT inside E.
What is conditional probability?
The probability that event B will occur given that event A has already.
Difference between the union and the intersection of two events
The union (E U F) refers to an event containing all outcomes in E, F or both
The intersection (E ∩ F) refers to an event that contains the outcomes ONLY in BOTH E and F
Why do we subtract the Intersect, P(E1 ∩ E2), from the Union, P(E1 ∪ E2), even though the intersect is INSIDE the union?
P(E1 ∪ E2) = P(E1) + P(E2) − P(E1 ∩ E2)
When we add each of the events (the circles), we account for the Intersection TWICE (once for each circle), so we have to subtract it afterwards.
How do we know if two events are independent?
Their probabilities do not influence each other. In other words, the probability of one happening does not change even if the other occurs first in sequence.
