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The Venn diagram below shows a sample space, S, of equally likely outcomes and events A and B. Find the following probabilities.     a. The probability of A:  P(A) b. The probability of B:  P(B) c. The probability of A 'given' B: P(A|B

The Venn diagram below shows a sample space, S, of equally likely outcomes and events A and B. Find the following probabilities.     a. The probability of A:  P(A) b. The probability of B:  P(B) c. The probability of A 'given' B: P(A|B

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The Venn diagram below shows a sample space, S, of equally likely outcomes and events A and B. Find the following probabilities.

 

 

a. The probability of A:  P(A)

b. The probability of B:  P(B)

c. The probability of A 'given' B: P(A|B)

d. The probability of B 'given' A: P(B|A)

This image depicts a Venn diagram illustrating the relationship between two sets, \(A\) and \(B\), within a universal set \(S\). - **Sets \(A\) and \(B\):** These are represented as two intersecting circles within a rectangular boundary, which symbolizes the universal set \(S\). - **Universal Set \(S\):** The rectangle surrounding the two circles, indicating the entire universe of possible elements for this context. - **Elements:** - The elements are shown as small blue dots. - Some dots are located inside circle \(A\) but outside circle \(B\), representing elements unique to set \(A\). - Some dots are inside circle \(B\) but outside circle \(A\), indicating elements unique to set \(B\). - The overlapping region of the circles contains dots that are common to both sets \(A\) and \(B\), representing the intersection of the two sets. - There are also dots outside both circles, but within the rectangle, indicating elements that are in the universal set but not in either set \(A\) or \(B\). This diagram helps in understanding concepts like union, intersection, and difference of sets.
Transcribed Image Text:This image depicts a Venn diagram illustrating the relationship between two sets, \(A\) and \(B\), within a universal set \(S\). - **Sets \(A\) and \(B\):** These are represented as two intersecting circles within a rectangular boundary, which symbolizes the universal set \(S\). - **Universal Set \(S\):** The rectangle surrounding the two circles, indicating the entire universe of possible elements for this context. - **Elements:** - The elements are shown as small blue dots. - Some dots are located inside circle \(A\) but outside circle \(B\), representing elements unique to set \(A\). - Some dots are inside circle \(B\) but outside circle \(A\), indicating elements unique to set \(B\). - The overlapping region of the circles contains dots that are common to both sets \(A\) and \(B\), representing the intersection of the two sets. - There are also dots outside both circles, but within the rectangle, indicating elements that are in the universal set but not in either set \(A\) or \(B\). This diagram helps in understanding concepts like union, intersection, and difference of sets.
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