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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 A E₂0 E₂ E30 Es B S 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 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(BA) P(ANB) P(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 A E₂0 E₂ E30 Es B S 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 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(BA) P(ANB) P(A)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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
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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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