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Q1. To examine if men and women have different attitudes towards risk, an investment firm has classified its clients according to their gender and to the composition of their investment portfolio. The firm classifies three types of investment portfolios: primarily bonds, primarily stocks, or a balanced mix of stocks and bonds. The proportions of clients falling into the various categories are shown in the following table: Portfolio Composition Gender Bonds Stocks Balanced Male 0.18 0.27 0.18 Female 0.12 0.10 0.15 One client is selected at random, and two events M and B are defined as follows: M: The selected client is Male. B: The selected client has a Balanced portfolio. A. What is P(M) ? (2 points) B. What is P(M | B) ? (2 points) C. What is P(M U B ) ? (2 points) D. Are events M and B independent? Explain. (4 points)