Chapter 14

The sample space is \(S=\\{1,2,3,4,5,6,\) 7,8,9,10}. Suppose that the outcomes are equally likely. Compute the probability of the event \(F=\\{3,5,9,10\\}\).

The sample space is \(S=\\{1,2,3,4,5,6,\) 7,8,9,10}. Suppose that the outcomes are equally likely. Compute the probability of the event \(E:\) "an even number."

How many three-digit numbers can be formed using the digits 0 and 1 ? Repeated digits are allowed.

As a financial planner, you are asked to select one stock each from the following groups: 8 Dow Jones stocks 15 NASDAO stocks, and 4 global stocks. How many different portfolios are possible?

The sample space is \(S=\\{1,2,3,4,5,6,\) 7,8,9,10}. Suppose that the outcomes are equally likely. Compute the probability of the event \(F:\) "an odd number."

How many three-digit numbers can be formed using the digits \(0,1,2,3,4,5,6,7,8,\) and \(9 ?\) Repeated digits are allowed.

An urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles. If one marble is selected, determine the probability that it is white.

In how many ways can 4 people be lined up?

Investigate the notion of counting as it relates to infinite sets. Write an essay on your findings.

An urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles. If one marble is selected, determine the probability that it is black.

In how many ways can 5 different boxes be stacked?

Graph \((x-2)^{2}+(y+1)^{2}=9\)

Assume equally likely outcomes. Determine the probability of having 3 boys in a 3 -child family.

How many different three-letter codes are there if only the letters \(A, B, C, D,\) and \(E\) can be used and no letter can be used more than once?

If the sides of a triangle are \(a=2, b=2,\) and \(c=3,\) find the measures of the three angles. Round to the nearest tenth.

Assume equally likely outcomes. Determine the probability of having 3 girls in a 3 -child family.

How many different four-letter codes are there if only the letters \(A, B, C, D, E,\) and \(F\) can be used and no letter can be used more than once?

Find all the real zeros of the function: $$ f(x)=(x-2)\left(x^{2}-3 x-10\right) $$

Assume equally likely outcomes. Determine the probability of having 1 girl and 3 boys in a 4 -child family.

Companies whose stocks are listed on the New York Stock Exchange (NYSE) have their company name represented by \(1,2,\) or 3 letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the NYSE?

Solve: \(\log _{3} x+\log _{3} 2=-2\)

Assume equally likely outcomes. Determine the probability of having 2 girls and 2 boys in a 4 -child family.

Companies whose stocks are listed on the NASDAQ stock exchange have their company name represented by either 4 or 5 letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the NASDAQ?

Solve: \(x^{3}=72 x\)

Two fair dice are rolled. Determine the probability that the sum of the faces is \(7 .\)

In how many ways can a committee of 4 students be formed from a pool of 7 students?

Solve the system: \(\left\\{\begin{array}{l}x-y=5 \\\ x-y^{2}=-1\end{array}\right.\)

Two fair dice are rolled. Determine the probability that the sum of the faces is \(11 .\)

In how many ways can a committee of 3 professors be formed from a department that has 8 professors?

Multiply: \((2 x-7)\left(3 x^{2}-5 x+4\right)\)

Two fair dice are rolled. Determine the probability that the sum of the faces is 3 .

How many arrangements of answers are possible for a true/false test with 10 questions?

Determine whether the infinite series converges or diverges. If it converges, find the sum. $$ 4+\frac{12}{5}+\frac{36}{25}+\frac{108}{125}+\ldots $$

Two fair dice are rolled. Determine the probability that the sum of the faces is \(12 .\)

How many arrangements of answers are possible in a multiple-choice test with 5 questions, each of which has 4 possible answers?

If \(f^{\prime \prime}(x)=\frac{2}{3}(x-2)^{-1 / 3}+\frac{1}{3}(x-2)^{-2 / 3},\) find where (a) \(f^{\prime \prime}(x)=0\) (b) \(f^{\prime \prime}(x)\) is undefined

Find the probability of the indicated event if \(P(A)=0.25\) and \(P(B)=0.45\) $$P(A \cup B) \text { if } P(A \cap B)=0.15$$

Five different mathematics books are to be arranged on a student's desk. How many arrangements are possible?

Find the partial fraction decomposition: \(\frac{3 x^{2}+15 x+5}{x^{3}+2 x^{2}+x}\)

Find the probability of the indicated event if \(P(A)=0.25\) and \(P(B)=0.45\) $$P(A \cap B) \text { if } P(A \cup B)=0.6$$

How many different license plate numbers can be made using 2 letters followed by 4 digits selected from the digits 0 through \(9,\) if: (a) Letters and digits may be repeated? (b) Letters may be repeated, but digits may not be repeated? (c) Neither letters nor digits may be repeated?

Find the probability of the indicated event if \(P(A)=0.25\) and \(P(B)=0.45\) $$P(A \cup B) \text { if } A, B \text { are mutually exclusive }$$

Find the probability of the indicated event if \(P(A)=0.25\) and \(P(B)=0.45\) $$P(A \cap B) \text { if } A, B \text { are mutually exclusive }$$

In how many ways can 5 people all have different birthdays? Assume that there are 365 days in a year.

$$\begin{array}{l}\text { If } P(A)=0.60, P(A \cup B)=0.85, \text { and } P(A \cap B)=0.05 \\\\\text { find } P(B) .\end{array}$$

A student dance committee is to be formed consisting of 2 boys and 3 girls. If the membership is to be chosen from 4 boys and 8 girls, how many different committees are possible?

$$\begin{array}{l}\text { If } P(B)=0.30, P(A \cup B)=0.65, \text { and } P(A \cap B)=0.15 \\\\\text { find } P(A) .\end{array}$$

The student relations committee of a college consists of 2 administrators, 3 faculty members, and 5 students. Four administrators, 8 faculty members, and 20 students are eligible to serve. How many different committees are possible?

According to the Insurance Information Institute, in 2016 there was a \(13.3 \%\) probability that an automobile theft in the United States would be cleared by arrests. If an automobile theft case from 2016 is randomly selected, what is the probability that it was not cleared by an arrest?

How many different 9-letter words (meaningful or not) can be formed from the letters in the word ECONOMICS?