Sam and Allen have applied for scholarships. The probability that Sam gets a scholarship is 0.93. The probability that Allen gets a scholarship is 0.77. The probability they both get scholarships is 0.74. (a) What is the probability that Sam gets a scholarship but Allen doesn't?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Sam and Allen have applied for scholarships. The probability that Sam gets a scholarship is 0.93. The probability that Allen gets a scholarship is 0.77. The probability they both get scholarships is 0.74.
(a) What is the probability that Sam gets a scholarship but Allen doesn't?
(b) What is the probability neither receives a scholarship?
(c) If Sam receives a scholarship, what then is the conditional probability that Allen will also receive a scholarship?
(d) If Allen receives a scholarship, what then is the conditional probability that Sam will not receive a scholarship?
Transcribed Image Text:Sam and Allen have applied for scholarships. The probability that Sam gets a scholarship is 0.93. The probability that Allen gets a scholarship is 0.77. The probability they both get scholarships is 0.74. (a) What is the probability that Sam gets a scholarship but Allen doesn't? (b) What is the probability neither receives a scholarship? (c) If Sam receives a scholarship, what then is the conditional probability that Allen will also receive a scholarship? (d) If Allen receives a scholarship, what then is the conditional probability that Sam will not receive a scholarship?
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