Independent events are events where the occurrence of one does not influence the probability of the other
P(A | B) = P(A) means the probability of A given that B has occurred is equal to the probability of A
True
For independent events A and B, if P(A) = 0.5 and P(B) = 0.5, then P(A and B) = 0.25
True
If P(A) = 13/52, then P(A) = 0.25
For independent events, P(A or B) = P(A) + P(B) - P(A)*P(B)
True
Two events A and B are independent if P(A and B) = P(A) * P(B)
If P(A | B) = P(A), then events A and B are independent
True
The joint probability of two independent events is the product of their individual probabilities
The probability of the union of events is calculated using the formula P(A∪B) = P(A) + P(B) - P(A∩B), where P(A∩B) is the probability of their intersection
What is the value of P(A | B) if events A and B are independent?
P(A)
The addition rule for unions of events states that P(A∪B) = P(A) + P(B) - P(A∩B), where P(A∩B) is the probability of their intersection
The formula for the addition rule is `P(A or B) = P(A) + P(B) - P(A and B
For independent events, P(A and B) = P(A) * P(B
The probability of a union of events is calculated using the formula `P(A or B) = P(A) + P(B) - P(A and B
The key properties of independent events include P(A \| B) = P(A)
For independent events, P(A and B) is calculated as P(A) * P(B)
The joint probability of independent events is the product of their individual probabilities
For independent events, P(A | B) = P(A)
True
The probability that both A and B occur for independent events is the product of their individual probabilities
True
The union of events, denoted as A∪B, includes all outcomes that belong to either event A or event B
For a union of events, if P(A) = 0.25, P(B) = 0.0769, and P(A∩B) = 0.0192, then P(A∪B) ≈ 0.3077
True
For independent events, P(A and B) = P(A)*P(B)
If P(A and B) = P(A) * P(B), then events A and B are independent
True
For independent events, P(A and B) = P(A) * P(B)
True
Flipping a coin twice results in independent events.
True
If P(A) = 1/6 and P(B) = 1/2, and A∩B occurs when rolling a 2, what is P(A∪B)?
1/2
For independent events, P(A and B) = P(A) * P(B).
True
If P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.2, what is P(A or B)?
0.7
What is the value of P(A or B) if P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.2?
0.7
What is the value of P(A and B) for independent events if P(A) = 1/6 and P(B) = 1/6?
1/36
What is the value of P(A or B) if P(A) = 0.25, P(B) ≈ 0.0769, and P(A and B) ≈ 0.0192?
0.3077
What does it mean for two events to be independent?
Occurrence of one does not influence the other
What is the definition of independent events in comparison to dependent events?
Occurrence of one does not affect the other
What is the key difference in the formula for joint probability between independent and dependent events?
P(A and B) = P(A) * P(B)
The addition rule calculates the probability of the union
If P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.2, then P(A or B) = 0.7.
True
When rolling a six-sided die, the probability of rolling a 3 is 1/6.
True
Match the probability concepts with their formulas:
Union of events ↔️ P(A or B) = P(A) + P(B) - P(A and B)
Multiplication rule for independent events ↔️ P(A and B) = P(A) * P(B)
The probability of getting heads on the first flip and tails on the second flip is 0.25
What is the first step in solving combined probability problems involving unions of events?