2. Properties of the Conditional Probability Theorem: Let (N, »' , P) be a probability space. If Be where P(B)>0, then the function P( |B) is a probability function with domain= Proof: Exercise. According to the theorem, P( |B) is a probábility function with domain= s. Thus, it should satisfy the following properties: P(Ø|B) = o.
2. Properties of the Conditional Probability Theorem: Let (N, »' , P) be a probability space. If Be where P(B)>0, then the function P( |B) is a probability function with domain= Proof: Exercise. According to the theorem, P( |B) is a probábility function with domain= s. Thus, it should satisfy the following properties: P(Ø|B) = o.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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Proof the ff. answer the first one only.
![2. Properties of the Conditional Probability
Theorem: Let (n, . P) be a probability space. If Ber where P(B)>0, then the
function PC |B) is a probability function with domain=
Proof: Exercise.
According to the theorem, P( |B) is a probábility function with domain=st. Thus,
it should satisfy the following properties:
P(Ø|B) = 0.
If A1,A2....An are mutually exclusive, events then
Finite additivity:
P(A,UAU...UAJB) = P(A;|B) +P(Az]B) + ... + P(AB).
If A is an event then P(A°]B) = 1- P(A|B).
If A, and Az are events then P(A,- Az|B) = P(A,|B) - P(A,A2|B).
If A, and Az are events then P(A,UAz|B) = P(A,|B) + P(A2|B)- P(A,A2B).
If A, and Az are events and A,CAz then P(A,|B) <P(A2|B).
If A,, A2,....An are events then P(A,UA;U...UA,]B) < P(A,|B) +P(A2]B) +
+ P(A|B).
...
O O o 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F620bcf24-d397-4622-ae81-a60f31e5e4f7%2F7dc846e3-63c0-4650-bdcc-f63e8ebe277e%2Fvi9ddyc_processed.png&w=3840&q=75)
Transcribed Image Text:2. Properties of the Conditional Probability
Theorem: Let (n, . P) be a probability space. If Ber where P(B)>0, then the
function PC |B) is a probability function with domain=
Proof: Exercise.
According to the theorem, P( |B) is a probábility function with domain=st. Thus,
it should satisfy the following properties:
P(Ø|B) = 0.
If A1,A2....An are mutually exclusive, events then
Finite additivity:
P(A,UAU...UAJB) = P(A;|B) +P(Az]B) + ... + P(AB).
If A is an event then P(A°]B) = 1- P(A|B).
If A, and Az are events then P(A,- Az|B) = P(A,|B) - P(A,A2|B).
If A, and Az are events then P(A,UAz|B) = P(A,|B) + P(A2|B)- P(A,A2B).
If A, and Az are events and A,CAz then P(A,|B) <P(A2|B).
If A,, A2,....An are events then P(A,UA;U...UA,]B) < P(A,|B) +P(A2]B) +
+ P(A|B).
...
O O o 0
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