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1. Choose independently two numbers B and C at random from the interval [0,1] with uniform density. (This means that the point (B, C) is then chosen at random in the unit square. An event involving the rv's B,C is then a subset of the unit square, and its probability is just the area.)
Find the probability that(a) B + C < 1/2.(b) BC < 1/2.(c) B-C <1/2.(d) max{B, C} < 1/2.(e) min{B, C}< 1/2.(f) B < 1/2 and 1- C < 1/2.(g) conditions (c) and (f) both hold.(h) B2 + C2 < 1/2.(i) (B - 1/2)2 + (C-1/2)2 < 1/4.
Please response to the following: Reason each step and explain the mathematical mistake if there is one.
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