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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 department store sells sports shirts in three sizes (small, medium, and large), three patterns (plaid, print, and stripe), and two sleeve lengths (long and short). The accompanying tables give the proportions of shirts sold in the various category combinations.

a. What is the probability that the next shirt sold is a medium, long-sleeved, print shirt?

b. What is the probability that the next shirt sold is a medium print shirt?

c. What is the probability that the next shirt sold is a short-sleeved shirt? A long-sleeved shirt?

d. What is the probability that the size of the next shirt sold is the medium? That the pattern of the next shirt sold as a print?

e. Given that the shirt just sold was a short-sleeved plaid, what is the probability that its size was medium?

f. Given that the shirt just sold was a medium plaid, what is the probability that it was short-sleeved? Long-sleeved?

Consider randomly selecting a student at a large university, and let Abe the event that the selected student has a Visa card and Bbe the analogous event for MasterCard. Suppose that P(A)=.6 and P(B)=.4.

a. Could it be the case that P(A\( \cap \)B)=.5? Why or why not? (Hint:See Exercise 24.)

b. From now on, suppose that P(A\( \cap \)B)=.3. What is the probability that the selected student has at least one of these two types of cards?

c. What is the probability that the selected student has neither type of card?

d. Describe, in terms of Aand B, the event that the selected student has a Visa card but not a MasterCard, and then calculate the probability of this event.

e. Calculate the probability that the selected student has exactly one of the two types of cards.

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?

The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group-blood group combinations.

Suppose that an individual is randomly selected from the population, and define events by \({\rm{A = }}\)\{type A selected), \({\rm{B = }}\) (type B selected), and \({\rm{C = }}\) (ethnic group \({\rm{3}}\) selected).

a. Calculate\({\rm{P(A),P(C)}}\), and \({\rm{P(A{C}C)}}\).

b. Calculate both \({\rm{P(A}}\mid {\rm{C)}}\)and \({\rm{P(C}}\mid {\rm{A)}}\), and explain in context what each of these probabilities represents.

c. If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group\({\rm{1}}\)?
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