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Chapter 5: Problem 69

A mutual fund company offers its customers several different funds: a money market fund, three different bond funds, two stock funds, and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the different funds are as follows: $$ \begin{array}{lr} \text { Money market } & 20 \% \\ \text { Short-term bond } & 15 \% \\ \text { Intermediate-term bond } & 10 \% \\ \text { Long-term bond } & 5 \% \\ \text { High-risk stock } & 18 \% \\ \text { Moderate-risk stock } & 25 \% \\ \text { Balanced fund } & 7 \% \end{array} $$ A customer who owns shares in just one fund is to be selected at random. 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?

Short Answer

Expert verified
a. The probability that the selected individual owns shares in the balanced fund is 7%. \ b. The probability that the selected individual owns shares in a bond fund is 30%. \ c. The probability that the selected individual does not own shares in a stock fund is 57%.

Step by step solution

01

Probability of owning shares in the balanced fund

The problem states that 7% of all customers own shares in the balanced fund. Therefore, if a customer is chosen at random, the probability of them owning shares in the balanced fund is also 7%. Since probability is the ratio of the number of favourable outcomes to the total number of possible outcomes, this simply translates the percentage into a probability.
02

Probability of owning shares in a bond fund

In order to find the probability that the selected individual owns shares in a bond fund, you need to add the probabilities of owning shares in each individual bond fund. From the data given, 15% own shares in the short-term bond, 10% own shares in the intermediate-term bond and 5% own shares in the long-term bond. The total probability here would be 15% + 10% + 5% = 30%, so the probability of owning shares in any bond fund is 30%.
03

Probability of not owning shares in a stock fund

In this case, we need to calculate the probability of the customer not owning shares in a stock fund. This is simply 1 (representing 100%) minus the total percentage of customers who own shares in a stock fund. From the data given, 18% own shares in high-risk stock and 25% own shares in moderate-risk stock. Thus, the probability of not owning shares in a stock fund = 100% - (18% + 25%) = 100% - 43% = 57%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mutual Funds
Mutual funds are like baskets of investments where multiple investors pool their money together. The company managing the fund uses this pooled money to invest in a variety of assets like stocks, bonds, or other securities. By doing so, it allows individual investors to diversify their investments without needing to buy each security individually.
  • Money Market Funds: Typically invest in low-risk, short-term securities, providing liquidity and safety.
  • Bond Funds: Invest mainly in bonds, which can vary in terms of duration and risk.
  • Stock Funds: These focus on investing in stocks or equities. They vary in risk, from high-risk to moderate-risk.
  • Balanced Funds: Invest in a mix of stocks and bonds aiming for both growth and income.

The concept of mutual funds is appealing because it allows accessibility, diversification, and professional management. This can be an excellent choice for people who want to invest in the markets but do not want to choose the specific stocks or bonds themselves.
Probability Calculation
Probability is a branch of mathematics that measures the likelihood of something happening. In simpler terms, it helps us answer questions like "What are the chances?" When it comes to selecting investments in mutual funds, we can use probability to predict outcomes based on given percentages.

To calculate the probability of a specific event鈥攍ike owning shares in a balanced fund鈥攚e use the formula:\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \]Given that 7% of customers own shares in the balanced fund, the probability that a randomly selected customer owns a balanced fund is simply 7%. This 7% is a representation of the favorable outcomes out of all possible outcomes.

Probability helps investors identify the risks and potential returns of their choices, calculating various outcomes based on past or present scenarios. It is a crucial tool for managing and assessing investment strategies.
Types of Funds
The different types of mutual funds are categorized based on their investment focus, strategy, and risk level. This classification helps investors select funds that suit their individual risk tolerance and financial goals.

  • **Money Market Funds:** Suitable for conservative investors, focusing on short-term and low-risk investments.
  • **Bond Funds:** Include several subcategories like short-term, intermediate-term, and long-term bonds. Investors can select based on their income needs and interest rate outlook.
  • **Stock Funds:** Can be divided into high-risk and moderate-risk funds, appealing to those seeking growth through equity investment.
  • **Balanced Funds:** Offer a blend of fixed income and growth-oriented investments, appealing to investors looking for a balanced risk-return profile.

Each type of fund provides different benefits and risks. By understanding these types, investors can make informed decisions about where to allocate their resources. It is crucial to align fund choices with personal financial goals and risk appetite.

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Most popular questions from this chapter

Phoenix is a hub for a large airline. Suppose that on a particular day, 8,000 passengers arrived in Phoenix on this airline. Phoenix was the final destination for 1,800 of these passengers. The others were all connecting to flights to other cities. On this particular day, several inbound flights were late, and 480 passengers missed their connecting flight. Of these 480 passengers, 75 were delayed overnight and had to spend the night in Phoenix. Consider the chance experiment of choosing a passenger at random from these 8,000 passengers. Calculate the following probabilities: a. the probability that the selected passenger had Phoenix as a final destination. b. the probability that the selected passenger did not have Phoenix as a final destination. c. the probability that the selected passenger was connecting and missed the connecting flight. d. the probability that the selected passenger was a connecting passenger and did not miss the connecting flight. e. the probability that the selected passenger either had Phoenix as a final destination or was delayed overnight in Phoenix. f. An independent customer satisfaction survey is planned. Fifty passengers selected at random from the 8,000 passengers who arrived in Phoenix on the day described above will be contacted for the survey. The airline knows that the survey results will not be favorable if too many people who were delayed overnight are included. Write a few sentences explaining whether or not you think the airline should be worried, using relevant probabilities to support your answer.

Roulette is a game of chance that involves spinning a wheel that is divided into 38 equal segments, as shown in the accompanying picture. A metal ball is tossed into the wheel as it is spinning, and the ball eventually lands in one of the 38 segments. Each segment has an associated color. Two segments are green. Half of the other 36 segments are red, and the others are black. When a balanced roulette wheel is spun, the ball is equally likely to land in any one of the 38 segments. a. When a balanced roulette wheel is spun, what is the probability that the ball lands in a red segment? b. In the roulette wheel shown, black and red segments alternate. Suppose instead that all red segments were grouped together and that all black segments were together. Does this increase the probability that the ball will land in a red segment? Explain. c. Suppose that you watch 1000 spins of a roulette wheel and note the color that results from each spin. What would be an indication that the wheel was not balanced?

An electronics store sells two different brands of DVD players. The store reports that \(30 \%\) of customers purchasing a DVD choose Brand \(1 .\) Of those that choose Brand \(1,20 \%\) purchase an extended warranty. Consider the chance experiment of randomly selecting a customer who purchased a DVD player at this store. a. One of the percentages given in the problem specifies an unconditional probability, and the other percentage specifies a conditional probability. Which one is the conditional probability, and how can you tell? b. Suppose that two events \(B\) and \(E\) are defined as follows: \(B=\) selected customer purchased Brand 1 \(E=\) selected customer purchased an extended warranty Use probability notation to translate the given information into two probability statements of the form \(P(\underline{ })=\) probability value.

The student council for a school of science and math has one representative from each of five academic departments: Biology (B), Chemistry (C), Mathematics (M), Physics (P), and Statistics (S). Two of these students are to be randomly selected for inclusion on a university-wide student committee. a. What are the 10 possible outcomes? b. From the description of the selection process, all outcomes are equally likely. What is the probability of each outcome? c. What is the probability that one of the committee members is the statistics department representative? d. What is the probability that both committee members come from laboratory science departments?

Lyme disease is the leading tick-borne disease in the United States and Europe. Diagnosis of the disease is difficult and is aided by a test that detects particular antibodies in the blood. The article "Laboratory Considerations in the Diagnosis and Management of Lyme Borreliosis" (American Journal of Clinical Pathology [1993]: \(168-174\) ) used the following notation: + represents a positive result on the blood test \- represents a negative result on the blood test \(L\) represents the event that the patient actually has Lyme disease \(L^{C}\) represents the event that the patient actually does not have Lyme disease The following probabilities were reported in the article:\(\begin{aligned} P(L) &=0.00207 \\ P\left(L^{C}\right) &=0.99793 \\ P(+\mid L) &=0.937 \\ P(-\mid L) &=0.063 \\ P\left(+\mid L^{C}\right) &=0.03 \\ P\left(-\mid L^{C}\right) &=0.97 \end{aligned}\) a. For each of the given probabilities, write a sentence giving an interpretation of the probability in the context of this problem. b. Use the given probabilities to construct a "hypothetical \(1000 "\) table with columns corresponding to whether or not a person has Lyme disease and rows corresponding to whether the blood test is positive or negative. c. Notice the form of the known conditional probabilities; for example, \(P(+\mid L)\) is the probability of a positive test given that a person selected at random from the population actually has Lyme disease. Of more interest is the probability that a person has Lyme disease, given that the test result is positive. Use the table constructed in Part (b) to calculate this probability.
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