Unit 4 Flashcards
What is empirical probability?
of successful trials / # total trials
This formula represents the likelihood of an event based on observed outcomes.
What does the Law of Large Numbers state?
More trials = closer to true probability
This law suggests that as the number of trials increases, the empirical probability will converge to the true probability.
What is a random process?
Any situation where we don’t know the outcome
Random processes are fundamental in probability theory as they involve uncertainty.
What is a sample space?
Set of all possible non-overlapping outcomes
The sample space encompasses every potential result of a random process.
How is the probability of an event E calculated?
P(E) = # of outcomes in favor of Event / Total # of outcomes in sample space
This formula quantifies the likelihood of event E occurring.
What is the range of probabilities?
Between 0 and 1
A probability of 0 indicates an impossible event, while a probability of 1 indicates a certain event.
What is the complement of an event?
The event not happening
The complement of event E is denoted as E^c, representing all outcomes where E does not occur.
What is the relationship between probability and repeated experiments?
Probability is defined through repeated experiments
This emphasizes that probability is not just a theoretical concept but is determined through actual trials.
What are mutually exclusive events?
Events that cannot occur at the same time.
What is the joint probability formula?
P (A and B) = P (A ∩ B)
What is the value of P (A and B) for mutually exclusive events?
P (A and B) = P (A ∩ B) = 0
How can you determine if P(A ∩ B) is mutually exclusive?
Create a 2-way table.
What is conditional probability?
The probability that an event will happen given that another event has occurred.
What does P(A | B) represent?
The probability of A given B.
P(A | B) = ?
P(A ∩ B) / P(B)
Equation of independence
P(A ∩ B) = P(A) * P(B)
