All Flashcards
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 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.
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.