Question: Pick a point x at random (with uniform density) in the interval [0, 1]. Find the probability that x > 1/2, given that (a) x

Pick a point x at random (with uniform density) in the interval [0, 1]. Find the probability that x > 1/2, given that
(a) x > 1/4.
(b) x < 3/4.
(c) |x − 1/2| < 1/4.
(d) x2 − x + 2/9 < 0.

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