What is Conditional Probability?
Conditional Probability And Independence

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Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
The probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads 'the probability of A given B'.
2.
FLASHCARD QUESTION
Front
What is the formula for Conditional Probability?
Back
P(A|B) = P(A and B) / P(B), provided P(B) > 0.
3.
FLASHCARD QUESTION
Front
What does it mean for two events to be independent?
Back
Two events A and B are independent if the occurrence of one does not affect the probability of the other. Mathematically, P(A|B) = P(A) and P(B|A) = P(B).
4.
FLASHCARD QUESTION
Front
How do you calculate the probability of two independent events both occurring?
Back
For independent events A and B, the probability of both occurring is P(A and B) = P(A) * P(B).
5.
FLASHCARD QUESTION
Front
What is the Law of Total Probability?
Back
If B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).
6.
FLASHCARD QUESTION
Front
What is the Complement Rule in probability?
Back
The probability of an event not occurring is 1 minus the probability of the event occurring: P(A') = 1 - P(A).
7.
FLASHCARD QUESTION
Front
How do you find P(A and B) for dependent events?
Back
For dependent events, P(A and B) = P(A) * P(B|A).
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