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Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.22. The probability of receiving both scholarships is 0.14. The probability of getting at least one of the scholarships is 0.35. (a) What is the probability that you will receive a Merit scholarship? (b) Are Events A and M mutually exclusive? Why or why not? Explain. Yes, because P(A nM) = 0. Yes, because P(AM) = 0. O No, because P(A nM) + 0. O No, because P(A nM) = 0. (c) Are Events A and M independent? Explain using probabilities.

Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.22. The probability of receiving both scholarships is 0.14. The probability of getting at least one of the scholarships is 0.35. (a) What is the probability that you will receive a Merit scholarship? (b) Are Events A and M mutually exclusive? Why or why not? Explain. Yes, because P(A nM) = 0. Yes, because P(AM) = 0. O No, because P(A nM) + 0. O No, because P(A nM) = 0. (c) Are Events A and M independent? Explain using probabilities.

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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Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.22. The probability of receiving both scholarships is 0.14. The probability of getting at least one of the scholarships is 0.35. (a) What is the probability that you will receive a Merit scholarship? (b) Are Events A and M mutually exclusive? Why or why not? Explain. Yes, because P(A N M) = 0. Yes, because P(AN M) + 0. No, because P(AN M) + 0. No, because P(AN M) = 0. (c) Are Events A and M independent? Explain using probabilities. Yes, because P(A N M) = P(A)P(M). Yes, because P(A N M) ‡ P(A)P(M). No, because P(A N M) ‡ P(A)P(M). No, because P(AN M) = P(A)P(M). (d) What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? (Round your answer to four decimal places.) (e) What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship? (Round your answer to four decimal places.) Need Help? Read It
Transcribed Image Text:Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.22. The probability of receiving both scholarships is 0.14. The probability of getting at least one of the scholarships is 0.35. (a) What is the probability that you will receive a Merit scholarship? (b) Are Events A and M mutually exclusive? Why or why not? Explain. Yes, because P(A N M) = 0. Yes, because P(AN M) + 0. No, because P(AN M) + 0. No, because P(AN M) = 0. (c) Are Events A and M independent? Explain using probabilities. Yes, because P(A N M) = P(A)P(M). Yes, because P(A N M) ‡ P(A)P(M). No, because P(A N M) ‡ P(A)P(M). No, because P(AN M) = P(A)P(M). (d) What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? (Round your answer to four decimal places.) (e) What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship? (Round your answer to four decimal places.) Need Help? Read It
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