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.
