Five companies (A, B, C, D, and E) that make electrical relays compete each year to be the sole supplier of relays to a major automobile manufacturer. The auto company's records show that the probabilities of choosing a company to be the sole supplier are Supplier chose: Probability: A B C D E 0.30 0.20 0.10 0.25 0.15 These events form a partition of the sample space S (see pg 17 of the 5.1-5.4 notes). (a) Draw a venn diagram that represents these events. (b) Suppose that supplier E goes out of business this year, leaving the remaining 4 companies to compete with one another. What are the new probabilities of companies A, B, C, and D being chosen as the sole supplier this year? Find the probability and express it using correct mathematical notation. Note: use conditional probabilities.