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A number x is selected at random in the interval [-1, 2]. Let the events A...

A number x is selected at random in the interval [-1, 2]. Let the events A = {x<0} and B = {|x-0.5|<0.5}, and C = {x >0.75} (a) Find the probabilities of A, B, AB and AC. (b) Find the probabilities of AuB, AuC and AuBuC by using the appropriate axioms or corollaries.

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Answer #1

The pdf of X is

(a)

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Now,

So,

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(b)

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