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Explain the concept of joint probability.
The likelihood of two events both occurring. It's the intersection of two events.
Explain the concept of mutually exclusive events.
Events that cannot occur simultaneously. If one happens, the other cannot.
What is the significance of P(A and B) = 0 for mutually exclusive events?
It indicates that events A and B have no common outcomes; they cannot happen at the same time.
Explain the addition rule's limitation.
The addition rule P(A or B) = P(A) + P(B) only applies when events A and B are mutually exclusive.
Explain why P(A or B) is less than 0.5 if A and B are not mutually exclusive in Practice Problem #1.
Because you'd need to subtract the probability of the intersection to avoid double counting.
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.