2]. Let the events A = {x < 0}, A number X is selected at random in the interval B = {\x – 0.5| < 0.5}, and C = {x > 0.75}. (a) Find the probabilities of A, B, A N B, and A Nc. (b) Find the probabilities of AU B, AUC, and AU BUC, first, by directly evaluating the sets and then their probabilities, and second, by using the appropriate axioms or %3D corollaries.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A number x is selected at random in the interval [-1, 2]. Let the events A = {x < 0},
B = {\x – 0.5| < 0.5}, and C = {x > 0.75}.
(a) Find the probabilities of A, B, AN B, and ANC.
(b) Find the probabilities of AU B, AUC, and AUBUC, first, by directly evaluating
the sets and then their probabilities, and second, by using the appropriate axioms or
corollaries.
Transcribed Image Text:A number x is selected at random in the interval [-1, 2]. Let the events A = {x < 0}, B = {\x – 0.5| < 0.5}, and C = {x > 0.75}. (a) Find the probabilities of A, B, AN B, and ANC. (b) Find the probabilities of AU B, AUC, and AUBUC, first, by directly evaluating the sets and then their probabilities, and second, by using the appropriate axioms or corollaries.
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