Theorem 3.9. For two events A and B, P (AnB) = P(A) .P (B IA), P(A) > 0 = P (B) . P(A \B), P(B) >0 } zwhere P(B |A) represents conditional probability of occurrence of B when the event A has already happened and P(A IB) is the conditional probability of happening of A, given that B has already happened.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
icon
Related questions
Question

Prove the theorem

Theorem 3-9. For two events A and B,
Р (AnB) %3DP(А) .Р (В IA), Р(A) > 0
3D Р(B). Р(A \B), Р(B) > 0
whère P(B \A) represents conditional probability of occurrence of B when the event A has
already happened and P(A |B) is the conditional probability of happening of A, given that
B has already happened.
Transcribed Image Text:Theorem 3-9. For two events A and B, Р (AnB) %3DP(А) .Р (В IA), Р(A) > 0 3D Р(B). Р(A \B), Р(B) > 0 whère P(B \A) represents conditional probability of occurrence of B when the event A has already happened and P(A |B) is the conditional probability of happening of A, given that B has already happened.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning