All Flashcards
Explain the concept of independence in probability.
Two events are independent if the outcome of one does not influence the outcome of the other. Knowing that one event has occurred provides no information about whether the other event will occur.
Explain the purpose of subtracting P(A and B) in the addition rule.
Subtracting P(A and B) avoids double-counting outcomes that are common to both events A and B when calculating P(A or B).
What is the definition of independent events?
Events where the occurrence of one does not affect the probability of the other.
What is a union of events?
The probability that event A or event B (or both) will occur. Denoted as A ∪ B.
Define P(A | B).
The conditional probability of event A occurring given that event B has already occurred.
What is the multiplication rule for independent events?
P(A and B) = P(A) * P(B)
What is the general addition rule?
P(A or B) = P(A) + P(B) - P(A and B)
If A and B are independent, what is P(A | B)?
P(A | B) = P(A)
If A and B are independent, what is P(B | A)?
P(B | A) = P(B)