B and C are each distributed uniformly, in other words f(x) = 1 if 0<=x<=1, and f(x) = 0 if otherwise.
This is a probability distribution function because it satisfies the two fundamental properties of
1. never being negative and
2. integrating to 1 (from negative infinity to positive infinity.)

a

Since the cdf of (B+C) between 0 and 1 is given by F(z) = (1/2)z2
then plugging in 1/2 and 0 for z and subtracting we get 0.125

b

Since the cdf of (BC) is given by F(z) = z - z log z
then plugging in 1/2 and 0 for z and subtracting we get 0.847

c

Since the cdf of |B-C| between 0 and 1 is given by F(z) = 1-(1-z)2
then plugging in 1/2 and 0 for z and subtracting we get 0.75

d

Since the cdf of max(B,C) between 0 and 1 is given by F(z) = z2
then plugging in 1/2 and 0 for z and subtracting we get 0.25

e

Since the cdf of min(B,C) between 0 and 1 is given by F(z) = 1-(1-z)2
then plugging in 1/2 and 0 for z and subtracting we get 0.75