# MATH 109 Lecture 4: Stats: Conditional Properties, Independent Events + Formulas

5.3

Conditional Probabilities- focus on just one group of objects and imagine taking a random

sample from that group alone.

KEYPOINT: In the study of conditional probabilities, P(A | B) means to find the probability

that Event A occurs, but to restrict your consideration to those outcomes of A that occur

within Event B. It means “the probability of A occurring, given that Event B has

occurred.”

Formula for Calculating Conditional Probabilities is:

Rule 5a: P(A | B) = P(B)

P(A AN D B)

Rule 5b: P(A AND

B) = P(B) P(A | B)

and also

P(A AND

B) = P(A) P(B | A)

★The line in the middle of Event A and Event B is not a division sign. It’s pronounced as

“given that.”

Probability Formula: P(A) = N(S)

N(A)

● Associated means “with.”

●Independent Events- we call variables or events that are not associated.

★When Events A and B are said to be independent, knowledge that Event B

occurred does not change the probability of Event A occurring.

★If these probabilities are equal, then the two events are independent. If they are

not equal, the two events are associated.

○ If the Event A and B are independent, to find the probability of Event A

AND

B, multiply the probability of A and the probability of B.

Formula for Independent Events:

P(A | B) = P(A)

Multiplication Rule

Rule 5c: P(A AND

B) = P(A) P(B)

## Document Summary

Conditional probabilities- focus on just one group of objects and imagine taking a random sample from that group alone. Keypoint: in the study of conditional probabilities, p(a | b) means to find the probability that event a occurs, but to restrict your consideration to those outcomes of a that occur within event b. It means the probability of a occurring, given that event b has occurred. Rule 5b: p(a and b) = p(b) p(a | b) P(a and b) = p(a) p(b | a) The line in the middle of event a and event b is not a division sign. Independent events - we call variables or events that are not associated. occurred does not change the probability of event a occurring. When events a and b are said to be independent, knowledge that event b. If these probabilities are equal, then the two events are independent.