B and C are both taken at random between 0 and 1 and there is an equal probability of being anywhere in that interval. That makes both of them uniform distributions on [0,1]. The density of a uniform is 1/b-a. With an interval of 1, that makes the density 1. If you integrate that, it becomes x from (1-0), which equals 1. This makes them a proper probability distribution.

(a) Pr(B + C < 1/2)

## [1] 0.128

## [1] 0.8466

## [1] 0.7538

## [1] 0.25

## [1] 0.7437