Probability Questions and Answers

A firm has classified its customers in two ways according to whether the account is overdue and whether the account is new less than 12 months or old An analysis of the firm s records provided the input for the following table of joint probabilities One account is selected at random A If the account is overdue what is the probability that it is new B If the account is new what is the probability that it is overdue Overdue Not overdue 0 03 New Old 0 51 0 15 0 31

Suppose that A and B are two events for which P A 0 21 P B 0 84 and P A and B 0 26 Find P AB P A B

A quick quiz consists of 4 multiple choice problems each of which has 4 answers only one of which is correct If you make random guesses on all 4 problems a What is the probability that all 4 of your answers are incorrect answer b What is the probability that all 4 of your answers are correct answer

There are 15 958 866 adults in a region If a polling organization randomly selects 1235 adults without replacement are the selections independent or dependent If the selections are dependent can they be treated as independent for the purposes of calculations CREZID Are the selections independent or dependent O A The selections are dependent because the selection is done without replacement OB The selections are independent because the selection is done without replacement OC The selections are dependent because the sample size is not small relative to the population OD The selections are independent because the sample size is small relative to the population

When randomly selecting adults let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes W does P MIB represent Is P MIB the same as P BIM What does P MIB represent OA The probability of getting a male given that someone with blue eyes has been selected OB The probability of getting a male and getting someone with blue eyes OC The probability of getting someone with blue eyes given that a male has been selected OD The probability of getting a male or getting someone with blue eyes

Fill in the blank The classical approach to probability requires that the outcomes are The classical approach to probability requires that the outcomes are

he sample space listing the eight simple events that are possible when a couple has three children is bbb bbg bgb bgg gbb gbg ggb ggg After identifying the ample space for a couple having four children find the probability of getting two girls and two boys in any order D dentify the sample space for a couple having four children bbbbbbbg bbgb bbgg bgbb bgbg bggb bggg gbbb gbbg gbgb gbgg ggbb ggbg gggb gggg Use a comma to separate answers as needed Find the probability of getting two girls and two boys in any order Type an integer or a decimal Do not round

It is impossible to get 5 aces when selecting cards from a shuffled deck Express the indicated degree of likelihood as a probability value between 0 and 1 inclu The probability is Type an integer or a decimal

O Skewed left O Symmetric Skewed right Uniform 8 9 5 7 4 58 000111222344566788 6789

Cell phone user Not a cell phone user Total O 30 1000 O 490 500 O 10 500 Speeding violation 30 500 10 20 30 No speeding violation 490 480 970 Total Consider the table above Find the probability of selecting a person with speeding violation GIVEN that he she is a cell phone user 500 500 1000

Suppose that three different closely related diseases A1 A2 and A3 occur in 25 15 and 12 of the population Find the probability of disease A2 given B3 using the table below O 0 44 O 0 23 0 30 0 28 Symptom State B B B B3 B4 no symptoms Disease State A A 08 18 06 68 A2 17 12 07 64 A3 10 14 08 68

80 O 86 O 86 5 22 86 5 O 87 Question 6 Consider the following dataset 77 79 80 86 87 87 94 99 Compute the range

Suppose a quiz consist of 3 questions with 2 possible answer choices What is the probability that you get exactly 1 question correct 0 5 O 0 375 O 0 125 O 0 05

The accompanying display shows the average drive distance in yards for 199 professional golfers during a week on a tour in a recent year Complete parts a through d below Click the icon to view the display a Describe this distribution The distribution is and b Approximately what proportion of professional golfers drive on average 280 yards or less OA 90 B 75 C 20 O D 50 E 1 c Estimate the mean by examining the histogram Choose the correct answer below O A 270 yards B 300 yards C 280 yards D 310 yards OE 290 yards d Should the mean be expected to be smaller than approximately equal to or larger than the median Why Display of Goters 30 25 20 15 10 54 260 270 280 200 300 Average Drive Length yd Print Done 310 320 odu Q G 1

The average score on the Stats midterm was 80 points with a standard deviation of 6 points and Karl s z score was 1 How many points did he score He scored points

3 1 Terminology 66 1200 1000 800 600 400 200 D 1045 40 60 Total Figure 3 20 82 70 18 34 138 41 59 226 45 55 268 49 51 55 64 331 48 52 65 478 35 44 45 54 Sample Percent approve Percent disapprove 44 56 Male 567 37 63 Female 100 096 The graph in Figure 3 20 displays the sample sizes and percentages of people in different age and gender groups who were polled concerning their approval of Mayor Ford s actions in office The total number in the sample of all the age groups is 1 045 a Define three events in the graph 6 Describe in words what the entry 40 means c Describe in words the complement of the entry in the previous question A d Describe in words what the entry 30 means e Out of the males and females what percent are males f Out of the females what percent disapprove of Mayor Ford g Out of all the age groups what percent approve of Mayor Ford h Find P Approve Male i Out of the age groups what percent are more than 44 years old J Find P Approve Age 35

3 2 Independent and Mutually Exclusive Events Use the following information to answer the next 12 exercises The graph shown is based on more than 170 000 interviews that took place from January through December 2012 The sample consists of employed Americans 18 years of age or older The Health Index Scores are the sample space We randomly sample one type of Health Index Score the emotional well being score Occupation Service Transportation Manufacturing or production Sales Clerical or office Installation and repair Construction or mining Manager executive or official Business owner Nurse Professional Farming fishing or forestry Teacher K 12 Physician Figure 3 21 77 78 79 80 Health Index Score 81 82 83 84 85 68 Find the probability that a Health Index Score is 82 7 69 Find the probability that a Health Index Score is 81 0 70 Find the probability that a Health Index Score is more than 81 71 Find the probability that a Health Index Score is between 80 5 and 82 72 If we know a Health Index Score is 81 5 or more what is the probability that it is 82 7 73 What is the probability that a Health Index Score is 80 7 or 82 7 74 What is the probability that a Health Index Score is less than 80 2 given that it is already less than 81 75 What occupation has the highest Health Index Score 76 What occupation has the lowest emotional index score 77 What is the range of the data

31 Don t stop exercising An investigation of the effect of different levels of physical activity was conducted on identical male twins in Finland For each twin pair al though they had maintained the same activity level for most of their lives one twin had significantly reduced his or her activity over the last few years due to work or family pressures For each pair of twins body fat per centage endurance levels and insulin sensitivity were measured For the less active twin the results showed greater body fat worse endurance and levels of insulin sensitivity displaying early signs of metabolic disease 23 a What type of design is being used in this investiga tion Give the explanatory and response variables b Is this an experiment or an observational study Why c The article reports that the measurements were car

13 Healthy Diet and Cataracts The relationship between healthy diet and prevalence of cataracts was assessed using a sample of 1808 participants from the Women s Health Initiative Observational Study Having a high Healthy Eat ing Index score was the strongest predictor of a reduced risk of cataracts among modifiable behaviors considered The Healthy Eating Index score was created by the U S Department of Agriculture and measures how well a person s diet con forms to recommended healthy eating patterns The report concludes These data add to the body of evidence suggesting that eating foods rich in a variety of vitamins and minerals may contribute to postponing the occurrence of the most common type of cataract in the United States 12 a Explain why this is an observational study rather than an experiment b Although the result was statistically significant the authors did not use strong language in stating their conclusions instead using words such as suggesting and may Do you think that their language is appropriate given the nature of the study Why

A hair salon surveyed 360 customers 100 females and 260 males to see if they are satisfied with the service The result is summarized in the following table Satisfied Not Satisfied Total Female 71 Male 219 Total 290 29 41 70 100 260 360 Type numbers in the boxes Part 1 10 points aby Part 2 10 points aby Part 3 10 points 30 points 1 If a customer is randomly selected from these 360 people the probability that he she is satisfied is Please round your answer to two decimal places 2 If we know the selected customer is a female then what is the probability that she is satisfied Please round your answer to two decimal positions P satisfied female 3 How about the probability that a randomly selected customer is a female if we know that the person is satisfied Please round your answer to two decimal positions

The probabilities for the amount that can be won on a lottery game are given in the table below Type numbers in the boxes Find the missing probability X 10 points Amount o 1 23 Probability 0 5 0 27 X 0 04 3 0 01

To plan for retirement Justin deposits 295 each quarter in an annuity that pays 7 interest compounded quarterly Payments will be made at the end of each quarter Find the total value of the annuity in 28 years Do not round any intermediate computations and round your final answer to the nearest cent If necessary refer to the list of financial formulas

The following data represents the GPA of a sample of 15 students enrolled in a history clas 3 4 3 9 4 0 2 8 3 5 2 6 3 2 3 6 1 9 2 1 2 0 3 3 2 4 1 8 3 2 a Find the first quartile Do not include the median in the calculations Answer b Find the third quartile Do not include the median in the calculations Answer c Find the mean Round to 2 decimal places

Data was collected for a sample of organic snacks The amount of sugar in mg in each snack is summarized in the histogram below Which statement best describes the meaning of one of the bars in the histogram Frequency 10 8 6 4 2 220 224 228 232 236 240 244 248 amount of sugar mg O246 snacks have 1 mg of sugar 1 snacks have about 246 mg of sugar O246 snacks have between 244 and 248 mg of sugar The largest number of snacks have 11 mg of sugar

Given below are data that has approximately normal distribution data data data data 57 28 41 18 44 35 46 67 53 82 47 62 71 23 39 82 54 88 58 04 53 63 41 68 42 3 40 61 39 41 47 99 45 58 78 03 60 83 48 95 65 81 41 29 40 67 51 43 44 44 56 37 45 47 47 72 51 84 58 93 54 24 48 73 63 93 69 49 69 13 62 21 59 45 39 92 60 65 In building a grouped frequency distribution table for this data set how many values are there in the clas 64 99 Include the lower class limit but not the upper class limit

Find the area under the standard O Answer Keypa Keyboard Shortc Normal Table to z Tables If you would like to look up the value in a table select the table you want to view then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key

A town recently dismissed 9 employees in order to meet their new budget reductions The town had 7 employees over 50 years of age and 18 under 50 If the dismissed employees were selected at random what is the probability that exactly 6 employees were over 50 Express your answer as a fraction or a decimal number rounded to four decimal places Answer ter your answer opens in new window Tables Keypad Keyboard Shortcuts

There are 8 black balls and 8 red balls in an urn If 4 balls are drawn without replacement what is the probability that exactly 1 black ball is drawn Express your answer as a fraction or a decimal number rounded to four decimal places Answer ndow Tables Keypad

There are 9 black balls and 6 red balls in an urn If 4 balls are drawn without replacement what is the probability that exactly 2 black balls are drawn Express your answer as a fraction or a decimal number rounded to four decimal places Answer llow to ont jour poor opens in new window Tables Keypad

A certain insecticide kills 80 of all insects in laboratory experiments A sample of 6 insects is exposed to the insecticide in a particular experiment What is the probability that exactly one insect will die Round your answer to four decimal places Answer down Tables

A certain insecticide kills 60 of all insects in laboratory experiments A sample of 7 insects is exposed to the insecticide in a particular experiment What is the probability that exactly 2 insects will survive Round your answer to four decimal places Answer Tables BEER

Assume the random variable X has a binomial distribution with the given probability of obtaining a success Find the following probability given the number of trials and the probability of obtaining a success Round your answer to four decimal places P X3 n 4 p 0 8

A researcher wishes to conduct a study of the color preferences of new car buyers Suppose that 50 of this population prefers the color red If 12 buyers are randoml selected what is the probability that exactly 2 buyers would prefer red Round your answer to four decimal places Answer How to enter your answer opens in new window Tables Keypad Keyboard Shortcu

Construct the discrete probability distribution for the random variable described Express the probabilities as simplified fractions The number of heads in 4 tosses of a coin Answer P X x 0 1 2 3 4 Tab

Consider the following data 2 P X x 0 3 Answer X Step 4 of 5 Find the value of P X 5 Round your answer to one decimal place 3 0 2 4 0 1 5 0 2 0 2 B 6

Minority Managers A firm wants to understand the attitudes of its minorit managers toward its system for assessing management performance Following is list of all the firm s managers who are members of minority groups Use the Simp Random Sample applet other software or Table B at line 127 to choose three man agers to be interviewed in detail about the performance appraisal system Modur Adelaja Ahmadiani Barnes Bonds Burke Deis Draguljic Fernandez Fox Gao Gemayel Gunta Huo Ippolito Jiang Jung Mani Morro Rettiganti Rodriguez Sanchez Sgambellone Voiimo

If an infinite number of random samples of size n are drawn from any population with mean u and standard deviation o then as the sample size n becomes large the sampling distribution of sample means will approach normality even if the population distribution is not normally distributed is known as the O central limit theorem normal distribution sampling distribution

A normal distribution curve is symmetric True False

A normal distribution curve peaks Once OTwice O Three times Four times

1 Researchers interviewed students and professors and asked them which type of entertainment they preferred books movies or video games The results are in the table below Students Professors Total Books Movies Video Games Total 21 15 38 6 18 51 27 33 89 a What fraction of the people in the study are students 38 89 2 27 29 b What fraction of the professors in the study preferred movies 18 51 c What fraction of the people who preferred books are students 21 27 d What fraction of the people in the study are professors who preferred video games 27 89 e Does there appear to be an association between role student professor and entertainment preference Explain

Select ALL systems that are equivalent to the one shown here 700 lb 25 A 1250 lb ft 3 5A 2 5A 1250 lb 4 2 5 ft B B 600 lb B 700 lb 1 ft Ift 1250 lb 2 5 ft 250 lb B 600 lb 500 lb 250 lb 2 5 ft 2 5 ft 500 lb 1250 lb B 1250 lb 1ft

The following distributed load can be replaced with a single resultant force where the magnitude is determined by FR L 2L 8L FR L 2 W FR L 21 8L FR L 2 Fr L 2L 8 Fr L 8L W 2x 8

Find the indicated probability A 6 sided die is rolled What is the probability of rolling a 4 or a 5 O 1 6 O 1 36 O the answer is none of these choices O 7 36

Answer the question considering an event to be unusual if its probability is less than or equal to 0 05 Assume that a study of 500 randomly selected school bus routes showed that 486 arrived on time Is it unusual for a school bus to arrive late O No O Yes

Find the indicated probability In a survey 306 respondents said they lived in an apartment and 626 said they lived in a house If one of the survey respondents is randomly selected find the probability of gettin someone who lives in an apartment Round to the nearest thousandth if necessary O the answer is none of these choices O 0 001 O 0 328

In a certain class of students there are 8 boys from Wilmette 6 girls from Kenilworth 9 girls from Wilmette 5 boys from Glencoe 5 boys from Kenilworth and 9 girls from Glencoe If the teacher calls upon a student to answer a question what is the probability that the student will be from Glencoe O the answer is none of these choices O 0 333 O 0 407 O 0 119 0 0314

Find the indicated probability If you pick a card at random from a well shuffled deck that contains no joker so 52 cards total what is the probability that you get a face card or a spade Assume that this deck contains 13 spades and there are 3 face cards that are spades jack queen and king there are 3 face cards that are hearts 3 face cards that are diamonds and 3 face cards that are clubs giving you a total of 12 face cards O 3 52 O 22 52 O the answer is none of these choices O 25 52

Find the indicated probability The table below describes the smoking habits of a group of asthma sufferers Smoking Habits of Asthma Sufferers Occasional Smoker 48 36 84 Men Women Total Nonsmoker Doesn t O 0 529 O 0 213 Smoke 435 320 755 Regular Smoker 76 74 150 Heavy Smoker 44 33 77 Total 603 463 1066 If one of the 1066 people is randomly selected find the probability of getting someone who is a regular or heavy smoker

Find the indicated probability A card is drawn from a well shuffled deck of 52 cards What is the probability of drawing an ace or a 7 O2 13 08 O 4 13 O 13 2

Cassie was the lucky journalist assigned to cover the Best Beard Competition She recorded the contestants beard colors in her notepad Cassie also noted if the contestants were signed up for the mustache competition later in the day Red beard Grey beard Only in the beard competition Also in the mustache competition 3 1 2 5 What is the probability that a randomly selected contestant is also in the mustache competition given that the contestant has a grey beard Simplify any fractions