Four economists have predicted the following rates of growth of GDP (%) for the next quarter:
E1 = below 2%, E2 = 2 or greater than 2% but below 4%, E3 = 4 or greater than 4% but less than 6%, and E4 = 6% or more.
Let Ai be the actual rate of % GDP growth rate according to the same four classifications as Ei (e.g., A1 = GDP growth rate of less than 2%).
a. Are the events E1 through E4 mutually exclusive? Are they collectively exhaustive?
b. What is the meaning of the events (1) E1A2 (or E1 ∩ A2), (2) E3 + A3 (or E3 ⋃ A3), (3) Ei + Ai (or Ei ⋃ Ai) where I = 1 through 4, and (4) EiAj (or Ei ∩ Aj) where i > j?