Solve the problem.The screens illustrate how the table feature of

Solve the problem.

The screens illustrate how the table feature of a graphing calculator can be used to find the probabilities of having 0, 1, 2, 3, or 4 girls in a family of 4 children. That 0 appears for values of x greater than 4 because these events are impossible.

Use the approach given on the previous page for the following.

(a) Find the probabilities of having 0, 1, 2, or 3 boys in a family of 3 children.

(b) Find the probabilities of having 0, 1, 2, 3, 4, 5, or 6 girls in a family of 6 children.

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The management of a firm wishes to survey the opinions

The management of a firm wishes to survey the opinions of its workers, classified as follows for the purpose of an interview: 30% have worked for the company 5 or more years, 28% are female, 65% contribute to a voluntary retirement plan, and 50% of the female workers contribute to the retirement plan.

Find each probability if a worker is selected at random.

(a) A male worker is selected.

(b) A worker is selected who has worked for the company less than 5 yr.

(c) A worker is selected who contributes to the retirement plan or is female.

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The table is an abbreviated version of the 2010 period

The table is an abbreviated version of the 2010 period life table used by the Office of the Chief Actuary of the Social Security Administration. (The actual table includes every age, not just every tenth age.) Theoretically, this table follows a group of 100,000 males at birth and gives the number still alive at each age. Round answers to the questions that follow to the nearest thousandth.

(a) What is the probability that a 40-year-old man will live 30 more years?

(b) What is the probability that a 40-year-old man will not live 30 more years?

(c) Consider a group of five 40-year-old men. What is the probability that exactly three of them survive to age 70?

(d) Consider two 40-year-old men. What is the probability that at least one of them survives to age 70?

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The numbers (in thousands) of foreign-born people who were living

The numbers (in thousands) of foreign-born people who were living in the United States in 2012, according to region of birth, are given in the table. Find the probability, to the nearest thousandth, that a foreign-born U.S. resident in 2012 satisfied the following in parts (a) –(c).

(a) Born in Asia

(b) Not born in Europe

(c) Born in Asia or Europe

(d) What are the odds that a randomly selected foreign-born U.S. resident was born in Latin America?

        Region …………………………Number (in thousands)

Asia …………………………………………..11,587

Europe ………………………………………11,596

Latin America …………………………….21,034

Other …………………………………………2809

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Write the event in set notation and give the probability

Write the event in set notation and give the probability of the event.

Associate each probability in parts (a)–(e) with one of the statements in choices A–E.

(a) P(E) = 0.01 

(b) P(E) = 1

(c) P(E) = 0.99

(d) P(E) = 0 

(e) P(E) = 0.5

A. The event is certain. 

B. The event is impossible.

C. The event is very likely to occur. 

D. The event is very unlikely to occur.

E. The event is just as likely to occur as not to occur.

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Write each event in set notation and give the probability

Write each event in set notation and give the probability of the event.

Refer to Exercise 10.

(a) Both slips are marked with even numbers.

(b) Both slips are marked with odd numbers.

(c) Both slips are marked with the same number.

(d) One slip is marked with an odd number, the other with an even number.

Exercise 10.

Slips of paper marked with the numbers 1, 2, 3, and 4 are placed in a box. A slip is drawn and set aside, its number is recorded, and then a second slip is drawn.

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There were 754,299 master’s degrees awarded in the United States

There were 754,299 master’s degrees awarded in the United States in 2012. The table shows the numbers of degrees awarded in several fields of study.

        Field of Study…………………………………………………………………….Number of Master’s Degrees

Business ……………………………………………………………………………………………103,253

Education…………………………………………………………………………………………..178,062

Health professions and related clinical studies …………………………………..83,893

Visual and performing arts …………………………………………………………………17,331

Other …………………………………………………………………………………………………371,760

(a) What is the probability that a randomly selected student who earned a master’s degree in 2012 earned a degree in business?

(b) What is the probability that a randomly selected student who earned a master’s degree in 2012 earned a degree in either health professions and related clinical studies or the visual and performing arts?

(c) What is the probability that a randomly selected student who earned a master’s degree in 2012 earned a degree that was not in education?

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Refer to Exercises 61 and 62. How much more will

Refer to Exercises 61 and 62. How much more will a person with 4 yr of college who earns the median amount make during his or her career than a person with no college attendance who earns the median amount during his or her career? If the expenses of a 4-yr college degree are estimated at $95,780, is earning a 4-yr college degree worth it?

Exercises 61.

In 2012 the median annual earnings of a high school graduate with no college attendance was $30,000. This amount is expected to increase by about $268 per year. 

Exercises 62.

In 2012 the median annual earnings of a person with 4 yr of college was $46,900. This amount is expected to increase by about $813 per year. 

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The current system of rating passers in the National Football

The current system of rating passers in the National Football League is based on four performance components: completions, touchdowns, yards gained, and interceptions, as percentages of the number of passes attempted. It uses the following formula.

where A = attempted passes, C = completed passes, T = touchdown passes, Y = yards gained passing, and I = interceptions.

In addition to the weighting factors appearing in the formula, the four category ratios are limited to nonnegative values with the following maximums.

Exercises give the 2014 regular-season statistics for the top twelve quarterbacks. Use the formula to determine the rating to the nearest tenth for each.

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Solve the problem.Consider the figure, which is a square divided

Solve the problem.

Consider the figure, which is a square divided into two squares and two rectangles.

(a) The length of each side of the largest square is x + y. Use the formula for the area of a square to write the area of the largest square as a power.

(b) Use the formulas for the area of a square and the area of a rectangle to write the area of the largest square as a trinomial that represents the sum of the areas of the four figures that make it up.

(c) Explain why the expressions in parts (a) and (b) must be equivalent.

(d) What special product formula from this section does this exercise reinforce geometrically?

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