Your broker has suggested that you diversify your investments by splitting your portfolio among mutual funds, municipal bond funds, stocks, and precious metals. She suggests three good mutual funds, four municipal bond funds, five stocks and three precious metals (gold, silver and platinum). 1) Assuming your portfolio is to contain one of each type of investment, how many portfolios are possible?   2) Assuming your portfolio is two contain rwo mutual funds, three municipal bond funds, one stock, and two precious metals, how many different portfolios are possible?

3. Modified Exercise 2.36 A restaurant offers three ways of paying the bill: cash, credit card, and mobile payment (e.g., Apple Pay, Google Wallet). At the end of the day there were 200 paid bills. Some of the bills were paid with a mix of cash, credit card, and mobile payment. There were 36 bills paid with cash, 82 bills paid with credit card, and 113 bills paid by mobile payment. There were 8 bills that used cash and credit card, 13 bills that used cash and mobile payment, and 15 bills that used credit card and mobile payment. Five of the bills were paid with all three methods. (a) If two distinct bills are chosen at random, what is the probability that at least one was paid using two or more methods? (b) Suppose that a bill chosen at random and was paid using two or more methods. What is the probability it was paid with all three methods? (c) If a bill is chosen at random, what is the probability that the bill was paid fully using only one of the methods? (d) Suppose that a bill…

A mutual fund company offers its customers a variety of funds: a money-market fund, three different bond funds (short, intermediate, and long-term), two stock funds (moderate and high-risk), and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the different funds are as follows. Money-market 25% High-risk stock 16% Short bond 14% Moderate-risk stock 25% Intermediate bond 6% Balanced 9% Long bond 5% A customer who owns shares in just one fund is randomly selected. (a) What is the probability that the selected individual owns shares in the balanced fund? (b) What is the probability that the individual owns shares in a bond fund? (c) What is the probability that the selected individual does not own shares in a stock fund?

An insurance company offers four different deductible levels-none,low, medium, and high-for its homeowner's policyholders and threedifferent levels-low, medium, and high-for its automobilepolicyholders. The accompanying table gives proportions for the variouscategories of policyholders who have both types of insurance. Forexample, the proportion of individuals with both low homeowner'sdeductible and low auto deductible is .06 (6% of all such individuals).   Homeowner's Auto N L M H LMH .04.07.02 .06.10.03 .05.20.15 .03.10.15 Suppose an individual having both types of policies is randomlyselected.a. What is the probability that the individual has a medium auto deductible and a high homeowner's deductible?b. What is the probability that the individual has a low autodeductible? A low homeowner's deductible?c. What is the probability that the individual is in the samecategory for both auto and homeowner's deductibles?d. Based on your answer in part (c), what is the probability…