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A sample space of size 50 is known to contain three events of importance. Event A contains 10 elements, event B contains 30 elements, and event C contains 25 elements. It is also known that no element can simultaneously occur in both events A and C.
a) What is the probability of the largest union of A and B? What about the largest union of B and C?
b) What is the probability of the largest intersection of A and B? What about the largest intersection of B and C?
c) Assume that the intersection of A and B is maximum, determine
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