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Sam and Allen have applied for scholarships. The probability that Sam gets a scholarship is 0.87. The probability that Allen gets a scholarship is 0.78. The probability they both get scholarships is 0.75.
(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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