probability with inequalities?

Question

I dont really need the answers here but could someone please explain the process in which the question can be done.

let x be a number that is selected randomly from the closed interval from 0 to 1 [0,1]. use your intuition to sign values to:

a) P({x: 0 <= x <=1/3})
b) P({x: 1/3 <= x <=1})
c) P({x: x = 1/3})
d) P({x: 1/2 < x < 5})

Answer 1

I interpret your notation to be asking in a) what is the probability that x will lie in the interval[0,1/3] when the total set of available numbers lies in the interval [0,1]. . Te answer would obviously be 1/3. If this is a correct interpretation, then the answer t b) would be 2/3, the answer to c) would be 0, and the answer to d would be 1/2.

Answer 2

a) P({x: 0 <= x <=1/3}) = 1/3
b) P({x: 1/3 <= x <=1}) = 2/3
c) P({x: x = 1/3}) = 0
d) P({x: 1/2 < x < 5}) = 1/2