Probability: Conditional, Independent and Dependent Events

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Mathematics
•
10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the definition of Conditional Probability?
Back
Conditional Probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which means the probability of A given B.
2.
FLASHCARD QUESTION
Front
What is the formula for Conditional Probability?
Back
The formula for Conditional Probability is P(A|B) = P(A and B) / P(B), where P(A and B) is the probability of both events occurring.
3.
FLASHCARD QUESTION
Front
What is the definition of Independent Events?
Back
Independent Events are two events where the occurrence of one event does not affect the occurrence of the other. For independent events A and B, P(A and B) = P(A) * P(B).
4.
FLASHCARD QUESTION
Front
What is the definition of Dependent Events?
Back
Dependent Events are two events where the occurrence of one event affects the occurrence of the other. For dependent events A and B, P(A|B) ≠ P(A).
5.
FLASHCARD QUESTION
Front
What does P(A or B) represent?
Back
P(A or B) represents the probability that either event A occurs, event B occurs, or both events occur. It is calculated using the formula P(A or B) = P(A) + P(B) - P(A and B).
6.
FLASHCARD QUESTION
Front
If P(A) = 0.4 and P(B) = 0.5, what is P(A and B) if A and B are independent?
Back
If A and B are independent, P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.
7.
FLASHCARD QUESTION
Front
What is the complement of an event?
Back
The complement of an event A, denoted as A', is the event that A does not occur. The probability of the complement is given by P(A') = 1 - P(A).
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