Consider the continuous sample space = [1, 1000]. For each event A in (A ), we define the probability P(A) to be

Consider the continuous sample space Ω = [1, 1000]. For each event A in Ω

(A ⊆ Ω), we define the probability P(A) to be k∕1000, where k is the number of integers included in the set A. Then:

(i) Show that P(⋅) satisfies the three properties of Definition 1.10.

(ii) Calculate the probabilities of the events

A = [100,200], B = [1, 100] U [900, 1000], C= C- [1001, 100 100i, 100i+ 2i+1 i=1