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3.57 Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E₁) = .20, P(E₂) = .30, P(E₁)=30, P(E₁).10, P(E₁).10 E₁ E E₂° E₂0 Es B S b. Suppose we know that event A has occurred, so that the reduced sample space consists of the three sample points in A-namely, E₁, E₂, and E₁. Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [i.e., P(B,A)]. Verify that the conditional probabilities are in the same proportion to one another as the original sample point probabilities. NW c.Calculate the conditional probability P(B|A) in two ways: (1) Add the adjusted (conditional) probabilities of the sample points in the intersection An B, as these represent the event that B occurs given that A has occurred; (2) use the formula for conditional probability: P(ANB) P(A) Verify that the two methods yield the same result. d. Are events A and B independent? Why and why not? P(B|A)=

3.57 Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E₁) = .20, P(E₂) = .30, P(E₁)=30, P(E₁).10, P(E₁).10 E₁ E E₂° E₂0 Es B S b. Suppose we know that event A has occurred, so that the reduced sample space consists of the three sample points in A-namely, E₁, E₂, and E₁. Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [i.e., P(B,A)]. Verify that the conditional probabilities are in the same proportion to one another as the original sample point probabilities. NW c.Calculate the conditional probability P(B|A) in two ways: (1) Add the adjusted (conditional) probabilities of the sample points in the intersection An B, as these represent the event that B occurs given that A has occurred; (2) use the formula for conditional probability: P(ANB) P(A) Verify that the two methods yield the same result. d. Are events A and B independent? Why and why not? P(B|A)=

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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Only part c and d please 

a. Calculate P(A), P(B), and P(AB) b. Suppose we know that event A has occurred, so that the reduced sample space consists of the three sample points in A-namely, E₁, E₂, and E₁. Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [i.e., P(E: A)]. Verify that the conditional 3.57 Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E₁).20, P(E₂) = .30, P(E3) = .30, P(E₁).10, P(E)= .10 probabilities are in the same proportion to one another as the original sample point probabilities. NW c.Calculate the conditional probability P(B|A) in two ways: (1) Add the adjusted (conditional) probabilities of the sample points in the intersection An B, as these represent the event that B occurs given that A has occurred; (2) use the formula for conditional probability: E₁ • A E₂0 E₂ E30 Es B P(BA) d. Are events A and B independent? Why and why not? P(An B) P(A) Verify that the two methods yield the same result.
Transcribed Image Text:a. Calculate P(A), P(B), and P(AB) b. Suppose we know that event A has occurred, so that the reduced sample space consists of the three sample points in A-namely, E₁, E₂, and E₁. Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [i.e., P(E: A)]. Verify that the conditional 3.57 Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E₁).20, P(E₂) = .30, P(E3) = .30, P(E₁).10, P(E)= .10 probabilities are in the same proportion to one another as the original sample point probabilities. NW c.Calculate the conditional probability P(B|A) in two ways: (1) Add the adjusted (conditional) probabilities of the sample points in the intersection An B, as these represent the event that B occurs given that A has occurred; (2) use the formula for conditional probability: E₁ • A E₂0 E₂ E30 Es B P(BA) d. Are events A and B independent? Why and why not? P(An B) P(A) Verify that the two methods yield the same result.
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