All Flashcards
What are the differences between independent and mutually exclusive events?
Independent: Can occur at the same time. | Mutually Exclusive: Cannot occur at the same time.
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)
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).