An engineering firm is constructing power plants at three different sites. Define the events E1, E2, and E3 as follows: E1 = the plant at site 1 is completed by the contract date. E2 = the plant at site 2 is completed by the contract date. E3 = the plant at site 3 is completed by the contract date. For each part below, draw a rectangle for the sample space and inside a Venn diagram that depicts these three events as intersecting circles. Shade the region on the Venn diagram corresponding to each of the following events (you should have 3 rectangles total).

• (a) At least one plant is completed by the contract date.
• (b) None of the plants is completed by the contract date.
• (c) Exactly one of the three plants is completed by the contract date.