5. A telecommunications company classifies transmission calls by their duration as brief (

(> 3 minutes) and by their type as voice (V), data (D), or fax (F). From an extensive data base, the company has come up with the following probabilities for the category of a random (e.g. the next) transmission call.

(a) For each of the following events specify the category outcomes that belong to them, and find their probabilities using relation (2.4.1).
(i) E1 = the next call is a voice call.
(ii) E2 = the next call is brief.
(iii) E3 = the next call is a data call.
(iv) E4 = E1 ∪ E2, and E5 = E1 ∪ E2 ∪ E3.

(b) Recalculate the probability of E4 using part (1) of Proposition 2.4-2.

(c) Recalculate the probability of E5 using part (2) of Proposition 2.4-2.

Duration Type of Transmission Call V D F > 3 0.25 0.10 0.07