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CO A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probablities of the sample points are P(1) = 0.2, P(2) = 0.05, P(3) = 0.35, P(4) = 0.15, P(5) = 0.15, P(6) = 0.0999999999999999. Use the Venn diagram and the probabilities of the sample points to find: (a) P(A) = 6 (b) P(BC) = | (c) P(BC) =

CO A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probablities of the sample points are P(1) = 0.2, P(2) = 0.05, P(3) = 0.35, P(4) = 0.15, P(5) = 0.15, P(6) = 0.0999999999999999. Use the Venn diagram and the probabilities of the sample points to find: (a) P(A) = 6 (b) P(BC) = | (c) P(BC) =

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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What is P(B|C) and P(complement B|complement C)?
### Description of the Problem A sample space contains six sample points and events \( A \), \( B \), and \( C \) as shown in the Venn diagram below. The probabilities of the sample points are given as follows: - \( P(1) = 0.2 \) - \( P(2) = 0.05 \) - \( P(3) = 0.35 \) - \( P(4) = 0.15 \) - \( P(5) = 0.15 \) - \( P(6) = 0.09999999999999999 \) ### Venn Diagram Explanation The Venn diagram consists of three overlapping circles, each representing an event \( A \), \( B \), or \( C \): - The red circle corresponds to event \( A \). - The blue circle corresponds to event \( B \). - The green circle corresponds to event \( C \). Sample points are distributed in the sections of the circles as follows: 1. Point 1 is in the red circle only. 2. Point 2 is in the red circle only. 3. Point 3 is in the intersection of all three circles. 4. Point 4 is in the intersection of the blue and green circles, but outside the red. 5. Point 5 is in the intersection of the red and green circles, but outside the blue. 6. Point 6 is only in the green circle. ### Tasks Use the Venn diagram and the probabilities of the sample points to find: (a) \( P(A) = \_\_ \) (b) \( P(B' \cap C) = \_\_ \) (c) \( P(B \cap C) = \_\_ \)
Transcribed Image Text:### Description of the Problem A sample space contains six sample points and events \( A \), \( B \), and \( C \) as shown in the Venn diagram below. The probabilities of the sample points are given as follows: - \( P(1) = 0.2 \) - \( P(2) = 0.05 \) - \( P(3) = 0.35 \) - \( P(4) = 0.15 \) - \( P(5) = 0.15 \) - \( P(6) = 0.09999999999999999 \) ### Venn Diagram Explanation The Venn diagram consists of three overlapping circles, each representing an event \( A \), \( B \), or \( C \): - The red circle corresponds to event \( A \). - The blue circle corresponds to event \( B \). - The green circle corresponds to event \( C \). Sample points are distributed in the sections of the circles as follows: 1. Point 1 is in the red circle only. 2. Point 2 is in the red circle only. 3. Point 3 is in the intersection of all three circles. 4. Point 4 is in the intersection of the blue and green circles, but outside the red. 5. Point 5 is in the intersection of the red and green circles, but outside the blue. 6. Point 6 is only in the green circle. ### Tasks Use the Venn diagram and the probabilities of the sample points to find: (a) \( P(A) = \_\_ \) (b) \( P(B' \cap C) = \_\_ \) (c) \( P(B \cap C) = \_\_ \)
This image shows a Venn diagram consisting of three intersecting ovals labeled A, B, and C, each in different colors. - The red oval (A) contains the numbers: - 1 in the top left section - 2 in the bottom left section - 3 in the middle section, overlapping with the blue oval (B) - The blue oval (B) contains the numbers: - 4 in the top overlapping section with both red (A) and green (C) ovals - 5 in the bottom overlapping section with the green oval (C) - The green oval (C) contains the number: - 6 in the far right section Each number indicates a distinct segment or intersection in the diagram: - Number 1 and 2 are unique to set A. - Number 3 is in the intersection of sets A and B. - Number 4 is in the intersection of all three sets A, B, and C. - Number 5 is in the intersection of sets B and C. - Number 6 is unique to set C. This Venn diagram visually represents the relationships and intersections between the three sets.
Transcribed Image Text:This image shows a Venn diagram consisting of three intersecting ovals labeled A, B, and C, each in different colors. - The red oval (A) contains the numbers: - 1 in the top left section - 2 in the bottom left section - 3 in the middle section, overlapping with the blue oval (B) - The blue oval (B) contains the numbers: - 4 in the top overlapping section with both red (A) and green (C) ovals - 5 in the bottom overlapping section with the green oval (C) - The green oval (C) contains the number: - 6 in the far right section Each number indicates a distinct segment or intersection in the diagram: - Number 1 and 2 are unique to set A. - Number 3 is in the intersection of sets A and B. - Number 4 is in the intersection of all three sets A, B, and C. - Number 5 is in the intersection of sets B and C. - Number 6 is unique to set C. This Venn diagram visually represents the relationships and intersections between the three sets.
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