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Chapter 2: Q11E (page 64)

A mutual fund company offers its customers a varietyof 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 areas follows:

Money-market 20% High-risk stock 18%

Short bond 15% Moderate-risk stock 25%

Intermediate bond 10% Balanced 7%

Long bond 5%

A customer who owns shares in just one fund is randomlyselected.

a. What is the probability that the selected individualowns 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 0.07

b. The probability that the selected individual owns shares in a bond fund is 0.30

c. The probability that the selected individual does not owns shares in a stock fund is 0.57

Step by step solution

01

Given information

A mutual fund company offers a variety of funds; they are a money-market fund, three different bond funds (short, intermediate, and long-term), two stock funds (moderate and high-risk), and a balanced fund.

02

Compute the probability

a.

The percentage of customer who owns shares in the balanced funds is provided as 7%.

The probability that the selected individual owns shares in the balanced fund is given as,

\(\frac{7}{{100}} = 0.07\)

Therefore, the probability that the selected individual owns shares in the balanced funds is 0.07.

b.

The percentage of customer who owns shares in the short bond is provided as 15%.

The percentage of customer who owns shares in the intermediate bond is provided as 10%.

The percentage of customer who owns shares in the long bond is provided as 5%.

The probability that the selected individual owns shares in a bond fund is given as,

\(\begin{aligned}\frac{{15}}{{100}} + \frac{{10}}{{100}} + \frac{5}{{100}} &= \frac{{30}}{{100}}\\ &= 0.30\end{aligned}\)

Therefore, the probability that the selected individual owns shares in a bond fund is 0.30.

c.

The percentage of customer who owns shares in the high-risk stock fund is provided as 18%.

The percentage of customer who owns shares in the moderate-risk fund is provided as 25%.

The probability that the selected individual owns shares in a stock fund is given as,

\(\begin{aligned}\frac{{18}}{{100}} + \frac{{25}}{{100}} &= \frac{{43}}{{100}}\\ &= 0.43\end{aligned}\)

The probability that the selected individual does not owns shares in a stock fund is given as,

\(1 - 0.43 = 0.57\)

Therefore, the probability that the selected individual does not owns shares in a stock fund is 0.57.

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Most popular questions from this chapter

a. A lumber company has just taken delivery on a shipment of \({\rm{10,000 2 \times 4}}\)boards. Suppose that 20% of these boards (\({\rm{2000}}\)) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other. Let A 5 {the first board is green} and B 5 {the second board is green}. Compute \({\rm{P(A),P(B)}}\), and \({\rm{P(A}} \cap {\rm{B)}}\) (a tree diagram might help). Are \({\rm{A}}\) and \({\rm{B}}\) independent?

b. With \({\rm{A}}\) and \({\rm{B}}\) independent and \({\rm{P(A) = P(B) = }}{\rm{.2,}}\) what is \({\rm{P(A}} \cap {\rm{B)}}\)? How much difference is there between this answer and \({\rm{P(A}} \cap {\rm{B)}}\)part (a)? For purposes of calculating \({\rm{P(A}} \cap {\rm{B)}}\), can we assume that \({\rm{A}}\)and \({\rm{B}}\) of part (a) are independent to obtain essentially the correct probability?

c. Suppose the shipment consists of ten boards, of which two are green. Does the assumption of independence now yield approximately the correct answer for \({\rm{P(A}} \cap {\rm{B)}}\)? What is the critical difference between the situation here and that of part (a)? When do you think an independence assumption would be valid in obtaining an approximately correct answer to \({\rm{P(A}} \cap {\rm{B)}}\)?

For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warranty. Relevant probabilities are

\(\begin{aligned}{\rm{P(A) = }}{\rm{.75}}\;\;\;{\rm{P(B}}\mid {\rm{A) = }}{\rm{.9}}\;\;\;{\rm{P}}\left( {{\rm{B}}\mid {{\rm{A}}^{\rm{\cent}}}} \right){\rm{ = }}{\rm{.8}}\\{\rm{P(C}}\mid {\rm{A\c{C}B) = }}{\rm{.8}}\;\;\;{\rm{P}}\left( {{\rm{C}}\mid {\rm{A\c{C}}}{{\rm{B}}^{\rm{\cent}}}} \right){\rm{ = }}{\rm{.6}}\\{\rm{P}}\left( {{\rm{C}}\mid {{\rm{A}}^{\rm{\cent}}}{\rm{\c{C}B}}} \right){\rm{ = }}{\rm{.7}}\;\;\;{\rm{P}}\left( {{\rm{C}}\mid {{\rm{A}}^{\rm{\cent}}}{\rm{\c{C}}}{{\rm{B}}^{\rm{\cent}}}} \right){\rm{ = }}{\rm{.3}}\end{aligned}\)

Construct a tree diagram consisting of first-, second-, and third-generation branches, and place an event label and appropriate probability next to each branch. b. Compute \({\rm{P(A\c{C}B\c{C}C)}}\). c. Compute \({\rm{P(B\c{C}C)}}\). d. Compute \({\rm{P(C)}}\). e. Compute \({\rm{P(A}}\mid {\rm{B\c{C}C)}}\), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased

A wallet contains five \(10 bills, four \)5 bills, and six \(1 bills (nothing larger). If the bills are selected one by one in random order, what is the probability that at least two bills must be selected to obtain a first \)10 bill?

An experimenter is studying the effects of temperature, pressure, and type of catalyst on yield from a certain chemical reaction. Three different temperatures, four different pressures, and five different catalysts are under consideration.

a. If any particular experimental run involves the use of a single temperature, pressure, and catalyst, how many experimental runs are possible?

b. How many experimental runs are there that involve use of the lowest temperature and two lowest pressures?

c. Suppose that five different experimental runs are to be made on the first day of experimentation. If the five are randomly selected from among all the possibilities, so that any group of five has the same probability of selection, what is the probability that a different catalyst is used on each run?

One of the assumptions underlying the theory of control charting is that successive plotted points are independent of one another. Each plotted point can signal either that a manufacturing process is operating correctly or that there is some sort of malfunction.
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