Answers Concepts in Probability and StatisticsApplications of Probability

Applications of Probability — Test Answers

24 verified answers

Free Preview

Which probabilities are correct? Choose two correct answers.

cap p times open paren cap c divides cap b close paren is equal to 8 over 27

cap p times open paren cap A divides cap c close paren is equal to 2 thirds

cap p times open paren cap b divides cap A close paren is equal to 13 over 27

cap p times cap A is equal to 31 over 59

cap p times cap c is equal to 3 sevenths

Free Preview

Pedro has determined that the probability his shot will score in a lacrosse game is 0 point 3 0 What is the probability that he will score on two consecutive shots?

0 point 3 0

0 point 6 0

0 point 1 5

0 point 0 9

A bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. Two marbles are drawn from the bag. What is the approximate probability one of the chosen marbles is orange and one of the chosen marbles is green?

0 point 0 8 8 8 9

0 point 1 3 3 3 3

0 point 0 2 2 2 2

0 point 0 4 4 4 4

A security alarm requires a four-digit code. The code can use the digits 0 - 9 and the digits cannot be repeated. Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7 ?

the fraction with numerator open paren sub 2 cap p sub 1 close paren times open paren sub 9 cap p sub 3 close paren and denominator sub 10 cap p sub 4

the fraction with numerator open paren sub 10 cap p sub 1 close paren times open paren sub 9 cap p sub 3 close paren and denominator sub 10 cap p sub 4

the fraction with numerator open paren sub 2 cap c sub 1 close paren times open paren sub 9 cap c sub 3 close paren and denominator sub 10 cap c sub 4

the fraction with numerator open paren sub 10 cap c sub 1 close paren times open paren sub 9 cap c sub 3 close paren and denominator sub 10 cap c sub 4

Aaron, Bob, and Charlotte are running a race. Which event would be considered dependent?

determining the chance that Bob comes in first or third

determining which person begins on the inside lane

determining whose coach runs the stopwatch

determining first, second, and third place runners

In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red. If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?

2 thirds

1 eighth

1 half

3 fourths

A manager records the number of hours, cap x , each employee works on his or her shift and develops the probability distribution. Fifty people work for the manager. How many people work 4 hours per shift? Probability Distribution Hours Worked: cap x Probability: cap p times cap x 3 0 point 1 4 ? 5 0 point 1 4 6 0 point 3 7 0 point 3 6 8 0 point 0 6

Christina is randomly choosing three movies to take on vacation from nine action movies, seven science fiction movies, and four comedies. Which statement is true?

The probability that Christina will not choose all comedies can be expressed as 1 minus the fraction with numerator 4 cap c sub 3 and denominator 20 cap c sub 4 .

The probability that Christina will not choose all action movies can be expressed as 1 minus the fraction with numerator 9 cap c sub 3 and denominator 20 cap c sub 3 .

The probability that Christina will choose three action movies can be expressed as the fraction with numerator sub 20 mathrm cap c sub 3 and denominator sub 9 mathrm cap c sub 3 .

The probability that Christina will choose three comedies can be expressed as the fraction with numerator 1 and denominator sub 4 mathrm cap c sub 3 .

Which of the following is a valid probability distribution?

Image with description The bar graph is titled Probability Distribution A. The horizontal axis lists 0 to 6 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 3 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 6 bars on the graph, and all the bars have a uniform height of 0 point 2.

Image with description The bar graph is titled Probability Distribution B. The horizontal axis lists 0 to 6 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 4 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 6 bars on the graph. The first bar is at 1 and its height is 0 point 1, the second bar is at 2 and its height is 0 point 2, the 3rd bar is at 3 and its height is 0 point 3, the 4th bar is at 4 and its height is 0 point 3, the 5th bar is at 5 and its height is 0 point 2, and the 6th bar is at 6 and its height is 0 point 1.

Image with description The bar graph is titled as "Probability Distribution D". The horizontal axis ranges from 0 to 6 with increments of 1 and also labeled as X. The vertical axis ranges from 0 to 0 point 6 with increments of 0 point 1 and also labeled as a P subscript X of x. There are 5 bars on the coordinate plane. The first bar is located at 1 and its height is 0 point 2, the second bar is located at 2 and its height is 0 point 1, the third bar is located at 3 and its height is 0 point 1, the fourth bar is located at 4 and its height is 0 point 5, and the fifth bar is located at 6 and its height is 0 point 1.

Image with description The bar graph is titled Probability Distribution C. The horizontal axis lists 0 to 6 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 5 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 5 bars on the graph. The first bar is at 1 and its height is 0 point 1, the second bar is at 2 and its height is 0 point 2, the 3rd bar is at 3 and its height is 0 point 4, the 4th bar is at 5 and its height is 0 point 1, and the 5th bar is at 6 and its height is 0 point 1.

A spinner is divided into eight equal-sized sections, numbered from 1 to 8 , inclusive. What is true about spinning the spinner one time? Choose three correct answers.

If a subset cap A represents spinning a number less than 4 ,then cap A is equal to 1 comma 2 comma 3 comma 4 .

If a subset cap A represents the complement of spinning an odd number, then cap A is equal to 2 comma 4 comma 6 comma 8 .

If cap A is a subset of cap s , cap A could be start set 7 comma 8 comma 9 end set .

cap s is equal to 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8

If cap A is a subset of cap s , cap A could be start set 1 comma 2 comma 3 end set .

Dependent events can best be described as

a group of events whose later outcomes are affected by previous outcomes.

a group of events whose later outcomes are not affected by previous outcomes.

two or more events that do not have the same probabilities.

two or more events that have the same probabilities.

Will surveyed students at his school about whether they have ever gone snowboarding and whether they own a skateboard. He found that 35 of the 99 students who own a skateboard have snowboarded. Also, there were 13 students who have snowboarded but do not own a skateboard, and 147 students who have never gone snowboarding and do not own a skateboard. Which two-way table correctly displays these data?

Table with 4 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Have Snowboarded'; Column 3, 'Never Snowboarded'; Column 4, 'Total' Row 2: Column 1, 'Skateboard'; Column 2, '35'; Column 3, '64'; Column 4, '99' Row 3: Column 1, 'No Skateboard'; Column 2, '13'; Column 3, '147'; Column 4, '160' Row 4: Column 1, 'Total'; Column 2, '48'; Column 3, '211'; Column 4, '259'

Table with 4 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Have Snowboarded'; Column 3, 'Never Snowboarded'; Column 4, 'Total' Row 2: Column 1, 'Skateboard'; Column 2, '35'; Column 3, '99'; Column 4, '134' Row 3: Column 1, 'No Skateboard'; Column 2, '13'; Column 3, '147'; Column 4, '160' Row 4: Column 1, 'Total'; Column 2, '48'; Column 3, '246'; Column 4, '294'

Table with 4 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Have Snowboarded'; Column 3, 'Never Snowboarded'; Column 4, 'Total' Row 2: Column 1, 'Skateboard'; Column 2, '35'; Column 3, '13'; Column 4, '48' Row 3: Column 1, 'No Skateboard'; Column 2, '99'; Column 3, '147'; Column 4, '246' Row 4: Column 1, 'Total'; Column 2, '134'; Column 3, '160'; Column 4, '294'

Table with 4 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Have Snowboarded'; Column 3, 'Never Snowboarded'; Column 4, 'Total' Row 2: Column 1, 'Skateboard'; Column 2, '35'; Column 3, '13'; Column 4, '48' Row 3: Column 1, 'No Skateboard'; Column 2, '64'; Column 3, '147'; Column 4, '211' Row 4: Column 1, 'Total'; Column 2, '99'; Column 3, '160'; Column 4, '256'

A six-sided number cube is rolled twice. Which expression can be used to find cap p times open paren 5 comma then 3 close paren ?

1 fifth times 1 third

5 sixths times 3 sixths

1 sixth times 1 sixth

1 sixth times 1 fifth

Eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag. Subset cap A of the sample space represents the complement of the event in which the number 6 is drawn from the bag. Which shows subset cap A ?

cap A is equal to 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8

cap A is equal to 1 comma 2 comma 3 comma 4 comma 5 comma 7 comma 8

cap A is equal to 6

cap A is equal to 1 comma 3 comma 5 comma 7

Four seniors and six juniors are competing for four places on a quiz bowl team. What is the approximate probability that all four seniors will be chosen at random?

0 point 0 0 0 2 0

0 point 0 6 6 6 7

0 point 0 7 1 4 2

0 point 0 0 4 7 6

To the nearest whole percent, what is the probability that a randomly selected customer from Satellite Company cap y watches recorded shows more often than live television?

41 percent

83 percent

77 percent

59 percent

Which statement is true about whether cap A and cap b are independent events?

cap A and cap b are independent events because cap p times open paren cap A divides cap b close paren is equal to cap p times cap A is equal to 0 point 7 5 .

cap A and cap b are not independent events because cap p times open paren cap A divides cap b close paren is equal to 0 point 7 5 and cap p times cap A is equal to 0 point 1 6 .

cap A and cap b are independent events because cap p times open paren cap A divides cap b close paren is equal to cap p times cap A is equal to 0 point 1 6 .

cap A and cap b are not independent events because cap p times open paren cap A divides cap b close paren is equal to 0 point 1 6 and cap p times cap A is equal to 0 point 7 5 .

To the nearest tenth, what is the value of cap p times open paren cap c divides cap y close paren ?

0 point 5

0 point 8

0 point 4

0 point 7

The table shows the ages of houses to the nearest year in a neighborhood. Using the age of the houses as the random variable, cap x , which graph shows the probability distribution, cap p sub cap x times x , of a randomly chosen house?

Image with description The bar graph is titled as "Probability Distribution". The horizontal axis ranges from 0 to 4 with increments of 1 and labeled as x. The vertical axis ranges from 0 to 0 point 3 5 with increments of 0 point 0 5 and labeled as a P subscript X of x. There are 4 bars on the graph. The first bar is located at 1 and its height is 0 point 1 5, the second bar is located at 2 and its height is 0 point 2, the third bar is at 3 and its height is 0 point 2 5, and the fourth bar is located at 4 and its height is 0 point 3.

Image with description The bar graph is titled Probability Distribution. The horizontal axis lists 0 to 4 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 3 5 in increments of 0 point 0 5 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 1 and its height is 0 point 1 6, the second bar is at 2 and its height is 0 point 2 2, the 3rd bar is at 3 and its height is 0 point 2 8, and the 4th bar is at 4 and its height is 0 point 3 3.

Image with description The bar graph is titled as "Probability Distribution". The horizontal axis ranges from 0 to 4 with increments of 1 and also labeled as x. The vertical axis ranges from 0 to 0 point 4 5 with increments of 0 point 0 5 and labeled as a P subscript X of x. There are 4 bars on the graph. The first bar is located at 1 and its height is 0 point 1, the second bar is located at 2 and its height is 0 point 2, the third bar is located at 3 and its height is 0 point 3, and the fourth bar is located at 4 and its height is 0 point 4.

Image with description The bar graph is titled as "Probability Distribution". The horizontal axis ranges from 0 to 4 with increments of 1 and labeled as x. The vertical axis ranges from 0 to 0 point 1 4 with increments of 0 point 0 2 and labeled as a P subscript X of x. There are 4 bars on the graph. The first bar is located at 1 and its height is 0 point 6 5, the second bar is located at 2 and its height is 0 point 1, the third bar is located at 3 and its height is 0 point 1 2, and the fourth bar is located at 4 and its height is 0 point 1 3.

What is the probability that the spinner will land on a number greater than 4 or on a shaded section?

2 thirds

5 sixths

1 half

2 ninths

Did you find these answers helpful?

Applications of Probability — Test Answers

More from this Course

TRY EDGENUITY HACKS