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 ∩ M) = 0.Yes, because P(A ∩ M) ≠ 0. No, because P(A ∩ M) ≠ 0.No, because P(A ∩ M) = 0. (c) Are Events A and M independent? Explain using probabilities. Yes, because P(A ∩ M) = P(A)P(M).Yes, because P(A ∩ M) ≠ P(A)P(M). No, because P(A ∩ M) = P(A)P(M).No, because P(A ∩ 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.)
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 ∩ M) = 0.Yes, because P(A ∩ M) ≠ 0. No, because P(A ∩ M) ≠ 0.No, because P(A ∩ M) = 0. (c) Are Events A and M independent? Explain using probabilities. Yes, because P(A ∩ M) = P(A)P(M).Yes, because P(A ∩ M) ≠ P(A)P(M). No, because P(A ∩ M) = P(A)P(M).No, because P(A ∩ 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.)
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.2: Probability
Problem 48E: Quality Control To control the quality of their product, the Bright-Light Company inspects three...
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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 ∩ M) = 0.Yes, because P(A ∩ M) ≠ 0. No, because P(A ∩ M) ≠ 0.No, because P(A ∩ M) = 0.
(c)
Are Events A and M independent? Explain using probabilities.
Yes, because P(A ∩ M) = P(A)P(M).Yes, because P(A ∩ M) ≠ P(A)P(M). No, because P(A ∩ M) = P(A)P(M).No, because P(A ∩ 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.)
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VIEWStep 2: Calculation for the probability that you will receive a Merit scholarship
VIEWStep 3: Identification of the Events A and M mutually exclusive or not
VIEWStep 4: Identification of the Events A and M are independent or not
VIEWStep 5: Calculation for the conditional probability P(A|M)
VIEWStep 6: Calculation for the conditional probability P(M|A)
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