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1. P(A U B)= В A 2. value of F= C 3 value of D= 4. value of C= F 5. value of E= GIVEN: P(A)= .45 P(B)= .35 P(A N B)= .20

1. P(A U B)= В A 2. value of F= C 3 value of D= 4. value of C= F 5. value of E= GIVEN: P(A)= .45 P(B)= .35 P(A N B)= .20

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The image features a Venn diagram with two intersecting circles labeled A and B, set within a rectangle. The intersection of the circles is labeled D, with separate areas for C and E within each circle and area F outside both. Given: - \( P(A) = 0.45 \) - \( P(B) = 0.35 \) - \( P(A \cap B) = 0.20 \) To find: 1. \( P(A \cup B) \): This is the probability that event A or event B occurs. - Formula: \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \) - Calculation: \( 0.45 + 0.35 - 0.20 = 0.60 \) 2. Value of F: Represents the probability outside events A and B. - Formula: \( P(F) = 1 - P(A \cup B) \) - Calculation: \( 1 - 0.60 = 0.40 \) 3. Value of D: This is the probability of the intersection of A and B. - Given directly as \( P(A \cap B) = 0.20 \) 4. Value of C: This is the probability of only A occurring. - Formula: \( P(C) = P(A) - P(A \cap B) \) - Calculation: \( 0.45 - 0.20 = 0.25 \) 5. Value of E: This is the probability of only B occurring. - Formula: \( P(E) = P(B) - P(A \cap B) \) - Calculation: \( 0.35 - 0.20 = 0.15 \) Summary: - \( P(A \cup B) = 0.60 \) - Value of F = 0.40 - Value of D = 0.20 - Value of C = 0.25 - Value of E = 0.15
Transcribed Image Text:The image features a Venn diagram with two intersecting circles labeled A and B, set within a rectangle. The intersection of the circles is labeled D, with separate areas for C and E within each circle and area F outside both. Given: - \( P(A) = 0.45 \) - \( P(B) = 0.35 \) - \( P(A \cap B) = 0.20 \) To find: 1. \( P(A \cup B) \): This is the probability that event A or event B occurs. - Formula: \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \) - Calculation: \( 0.45 + 0.35 - 0.20 = 0.60 \) 2. Value of F: Represents the probability outside events A and B. - Formula: \( P(F) = 1 - P(A \cup B) \) - Calculation: \( 1 - 0.60 = 0.40 \) 3. Value of D: This is the probability of the intersection of A and B. - Given directly as \( P(A \cap B) = 0.20 \) 4. Value of C: This is the probability of only A occurring. - Formula: \( P(C) = P(A) - P(A \cap B) \) - Calculation: \( 0.45 - 0.20 = 0.25 \) 5. Value of E: This is the probability of only B occurring. - Formula: \( P(E) = P(B) - P(A \cap B) \) - Calculation: \( 0.35 - 0.20 = 0.15 \) Summary: - \( P(A \cup B) = 0.60 \) - Value of F = 0.40 - Value of D = 0.20 - Value of C = 0.25 - Value of E = 0.15
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