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20. P(A) = 0.40 P(B) = 0.25 P(AUB) = 0.50 Part a: Find P(ANB) Part b: Find P(A/B) Part c: Find P(BIA) Part d: Are events A and B independent? Proposed Solution: Part a: P(AnB) = P(A)*P(B) = 0.40 * 0.25 = 0.1 Part b: P(A/B) = P(AnB)/P(B) = 0.1/0.25 = 0.4 Part c: P(B|A) = P(A^B)/P(A) = 0.1/0.4 = 0.25 Part d: Yes, since P(A) = P(A|B); P(B) = P(B|A) What was done wrong in the proposed solution? A. P(A/B) = P(AUB)/P(B) and all other parts are using this answer. B. To show independence, you must verify P(A)*P(B) = P(AnB). C. The formula used to find P(AnB), in part a, only is valid for independent events which has not yet been shown. D. P(A/B) = P(ANB)/P(A), and a similar error for P(B|A). E. The proposed solution is correct.

20. P(A) = 0.40 P(B) = 0.25 P(AUB) = 0.50 Part a: Find P(ANB) Part b: Find P(A/B) Part c: Find P(BIA) Part d: Are events A and B independent? Proposed Solution: Part a: P(AnB) = P(A)*P(B) = 0.40 * 0.25 = 0.1 Part b: P(A/B) = P(AnB)/P(B) = 0.1/0.25 = 0.4 Part c: P(B|A) = P(A^B)/P(A) = 0.1/0.4 = 0.25 Part d: Yes, since P(A) = P(A|B); P(B) = P(B|A) What was done wrong in the proposed solution? A. P(A/B) = P(AUB)/P(B) and all other parts are using this answer. B. To show independence, you must verify P(A)*P(B) = P(AnB). C. The formula used to find P(AnB), in part a, only is valid for independent events which has not yet been shown. D. P(A/B) = P(ANB)/P(A), and a similar error for P(B|A). E. The proposed solution is correct.

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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20. P(A) = 0.40 P(B) = 0.25 P(AUB) = 0.50 Part a: Find P(ANB) Part b: Find P(A/B) Part c: Find P(BIA) Part d: Are events A and B independent? Proposed Solution: Part a: P(AnB) = P(A)*P(B) = 0.40 * 0.25 = 0.1 Part b: P(A|B) = P(AnB)/P(B) = 0.1/0.25 = 0.4 Part c: P(B|A) = P(AnB)/P(A) = 0.1/0.4 = 0.25 Part d: Yes, since P(A) = P(A|B); P(B) = P(B|A) What was done wrong in the proposed solution? A. P(A|B) = P(AUB)/P(B) and all other parts are using this answer. B. To show independence, you must verify P(A)*P(B) = P(ANB). C. The formula used to find P(AnB), in part a, only is valid for independent events which has not yet been shown. D. P(A/B) = P(ANB)/P(A), and a similar error for P(BIA). E. The proposed solution is correct.
Transcribed Image Text:20. P(A) = 0.40 P(B) = 0.25 P(AUB) = 0.50 Part a: Find P(ANB) Part b: Find P(A/B) Part c: Find P(BIA) Part d: Are events A and B independent? Proposed Solution: Part a: P(AnB) = P(A)*P(B) = 0.40 * 0.25 = 0.1 Part b: P(A|B) = P(AnB)/P(B) = 0.1/0.25 = 0.4 Part c: P(B|A) = P(AnB)/P(A) = 0.1/0.4 = 0.25 Part d: Yes, since P(A) = P(A|B); P(B) = P(B|A) What was done wrong in the proposed solution? A. P(A|B) = P(AUB)/P(B) and all other parts are using this answer. B. To show independence, you must verify P(A)*P(B) = P(ANB). C. The formula used to find P(AnB), in part a, only is valid for independent events which has not yet been shown. D. P(A/B) = P(ANB)/P(A), and a similar error for P(BIA). E. The proposed solution is correct.
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