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What is the formula for P(A or B) when A and B are mutually exclusive?
P(A or B) = P(A) + P(B)
If events are not mutually exclusive, how do you calculate P(A or B)?
P(A or B) = P(A) + P(B) - P(A and B)
What is the formula to find the probability of A or B happening?
P(A \cup B) = P(A) + P(B)
What is P(A|B) equal to?
P(A|B) = P(A and B) / P(B)
What is the formula for finding P(Sport or Club)?
P(Sport or Club) = P(Sport) + P(Club) - P(Sport and Club)
What is the definition of 'intersection' (joint probability)?
The probability that both events A and B happen at the same time. P(A and B) or P(A ∩ B).
What are mutually exclusive events?
Events that cannot happen at the same time. They have no outcomes in common.
What does P(A and B) equal if A and B are mutually exclusive?
P(A and B) = 0
Define independent events.
Events where the outcome of one event does not affect the probability of the other.
What is the addition rule for mutually exclusive events?
The probability of one or the other happening is the sum of their individual probabilities.
What are the differences between mutually exclusive and independent events?
Mutually Exclusive: Cannot occur at the same time. | Independent: One event doesn't affect the probability of the other.
Compare and contrast intersection and union of events.
Intersection: Both events occur. | Union: Either one or both events occur.
What is the difference between P(A and B) for mutually exclusive vs. independent events?
Mutually Exclusive: P(A and B) = 0 | Independent: P(A and B) = P(A) * P(B)
Compare the addition rule for mutually exclusive and non-mutually exclusive events.
Mutually Exclusive: P(A or B) = P(A) + P(B) | Non-Mutually Exclusive: P(A or B) = P(A) + P(B) - P(A and B)
Differentiate between mutually exclusive events and conditional probability.
Mutually Exclusive: Occurrence of one prevents the other. | Conditional Probability: Probability of one event given another has occurred.