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Questions and Answers
What is the probability of the intersection of two events A and B when they are independent?
What is the probability of the intersection of two events A and B when they are independent?
What does P(A ∩ B) represent?
What does P(A ∩ B) represent?
What is the definition of mutually exclusive events?
What is the definition of mutually exclusive events?
What is the formula for the probability of the intersection of two events A and B?
What is the formula for the probability of the intersection of two events A and B?
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What is the probability of the intersection of two mutually exclusive events A and B?
What is the probability of the intersection of two mutually exclusive events A and B?
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What does P(A|B) represent?
What does P(A|B) represent?
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When are two events A and B considered independent?
When are two events A and B considered independent?
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What is the probability of the union of two events A and B, denoted as A ∪ B?
What is the probability of the union of two events A and B, denoted as A ∪ B?
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What is the formula for the probability of the intersection of two independent events A and B?
What is the formula for the probability of the intersection of two independent events A and B?
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Study Notes
Probability of Union of Two Events
Intersection of Events
- The intersection of two events A and B, denoted as A ∩ B, represents the occurrence of both events.
- The probability of the intersection of two events is denoted as P(A ∩ B).
- The probability of the intersection of two events can be calculated using the formula:
P(A ∩ B) = P(A) × P(B|A) = P(B) × P(A|B)
Where P(A|B) is the conditional probability of event A given event B, and P(B|A) is the conditional probability of event B given event A.
Independent Events
- Two events A and B are said to be independent if the occurrence of one event does not affect the probability of the other event.
- If A and B are independent, then:
P(A ∩ B) = P(A) × P(B)
- In other words, the probability of the intersection of two independent events is the product of their individual probabilities.
Mutually Exclusive Events
- Two events A and B are said to be mutually exclusive if they cannot occur simultaneously.
- If A and B are mutually exclusive, then:
P(A ∩ B) = 0
- In other words, the probability of the intersection of two mutually exclusive events is zero.
Probability of Union of Two Events
- The probability of the union of two events A and B, denoted as A ∪ B, represents the occurrence of at least one of the events.
- The probability of the union of two events can be calculated using the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
- Note that if A and B are mutually exclusive, then P(A ∩ B) = 0, and the formula simplifies to:
P(A ∪ B) = P(A) + P(B)
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Description
Learn about the intersection and union of two events, independence, and mutual exclusivity in probability theory. Understand the formulas and concepts to calculate probabilities.
