16 flashcards · Shared on 19 August 2026 by AtomAI Library
Flip each card to check yourself.
What does it mean for two events A and B to be independent?
The occurrence of one event does not change the probability of the other
What does it mean for two events A and B to be independent?
The occurrence of one event does not change the probability of the other
Two events are mutually exclusive when:
they cannot both occur in the same trial
Which formula gives the conditional probability of A given B, assuming P(B) > 0?
P(A | B) = P(A ∩ B) / P(B)
For independent events A and B, which relationship must hold?
P(A ∩ B) = P(A)P(B)
If A and B are mutually exclusive, what is P(A ∩ B)?
0
Events A and B are mutually exclusive. If P(A) = 0.35 and P(B) = 0.40, what is P(A ∪ B)?
0.75
Two events are both independent and mutually exclusive. What must be true?
At least one of the events has probability 0
Given P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.3, what can be concluded?
A and B are independent
If P(A ∩ B) = 0.18 and P(B) = 0.30, what is P(A | B)?
0.60
Which formula is the general addition rule for two events?
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
A card is drawn from a standard deck, replaced, and then another card is drawn. Why can the two draws be treated as independent?
Replacement restores the original probabilities before the second draw
A card is drawn from a standard deck and not replaced before a second card is drawn. How are the two draws related?
They are dependent because the first draw changes the second draw's probabilities
If P(A | B) = 0.4 and P(B) = 0.5, what is P(A ∩ B)?
0.20
When A and B are independent and P(B) > 0, what is P(A | B)?
P(A)
A fair coin is tossed and a fair six-sided die is rolled. What is the probability of getting heads and rolling a 4?
1/12
For events A and B with P(B) > 0, which multiplication rule is always valid?
P(A ∩ B) = P(A | B)P(B)