Probability Questions and Answers

uate using a grapher calculator will display the answer CO

Question 7 9 1 17 GI HW Score 2 5 1 of 40 points O Points 0 of 1 on in a roulette game is to bet 22 on red There are 18 red compartments 18 black com ments that are neither red nor black If the ball lands on red you get to keep the 22 you d you are awarded 22 If the ball lands elsewhere you are awarded nothing and the 22 1 Find the expected payback for this roulette game if you bet 22 on red ected payback is Round to the nearest cent as needed

the expected value of the random variable 3 4 5 0 1 0 3 0 4 X P x Question 4 9 1 9 2 0 2 is the expected value Type an integer or a decimal

Part 3 of 3 ce is rolled Find the probability of rolling ot more than 4 ot less than 6 etween 5 and 10 exclusive points Points 0 33 of 1 a The probability of rolling at 4 is 6 Type an integer or a simplifi b The probability of rolling as 13 18 Type an integer or a simplifi is c The probability of rolling at 10 exclusive is Type an integer or a simplifi

Question 7 8 4 8 C of dice is rolled What is the probability of getting a sum of t is the probability of getting a sum of 11 your answer Type a fraction plify

Question 11 8 4 26 O Points Engle fair die is tossed Find the odds in favor of rolling a number greater at are the odds in favor of rolling a number greater than 4 to nplify your answer

single fair 6 sided die is tossed Find the odds in favor of rolling a hat are the odds in favor of rolling a 1 3 or 5 to mplify your answer

arble is drawn from a box containing 5 yellow 2 white and 10 blue marbles Find the wing yellow marble blue marble white marble reduced form the odds in favor of drawing a yellow marble are to plify your answers

ose a single fair die is rolled Find the probability that it is a 2 g robability is an integer or a simplified fraction O

Question 17 8 5 6 o fair dice are rolled find the probability of the following result A double given that the sum was 7 0 probability is Type an integer or a simplified fraction

following frequency table repre Hourly Wage at First Job Class 5 7 6 2 6 3 6 8 6 9 7 4 7 5 8 0 8 1 8 6 Determine the cumulative frequency for the fifth class Frequency 2 7 4 10 13

Q1 The P A B 0 4000 and the P A and B 0 3600 What is the P B C 0 9000 A 0 1440 B 0 7600 D 0 8120 E 0 4120 Q2 The probability that a senior at JHS is an honors student is 0 35 The probability that a senior at JHS is in at least one AP class is 0 20 The probability that a senior at JHS is an honors student and is in at least one AP class is 0 15 What is the probability that a senior at JHS is not an honors student and is not in at least one AP class B 0 60 C 0 80 A 0 65 D 0 35 E 0 45 Q3 The probability that a senior at JHS is an honors student is 0 35 The probability that a senior at JHS is in at least one AP class is 0 20 The probability that a senior at JHS is an honors student and is in at least one AP class is 0 15 What is the probability that a senior at JHS is an honors student or is in at least one AP class A 0 40 D 0 45 B 0 15 E 0 60 C 0 55

z Scores In Exercises 5 8 express all z scores with tw GG international airport The complete list of 50 Verizon data speeds has a mean of x 17 60 Data Speeds in Appendix B the highest speed of 77 8 Mbps was measured at Atlanta s ATL Mbps and a standard deviation of s 16 02 Mbps a What is the difference between Verizon s data speed at Atlanta s international airport and the mean of all of Verizon s data speeds b How many standard deviations is that the difference found in part a c Convert Verizon s data speed at Atlanta s international airport to a z score d If we consider data speeds that convert to z scores between 2 and 2 to be neither signifi antly low nor significantly high is Verizon s speed at Atlanta significant ging the Verizon data speed of 0 8 Mhna

Q4 The sample space of a probability process contains events H I J and K The events are mutually exclusive The P H 0 2 P I 0 4 P J 0 3 and P K 0 1 What is the probability of H and I A 0 08 B 0 6 C 0 D 0 75 E 0 50 Q5 The P S 50 and the P T 35 The events are independent What is the probability that the events occur at the same time A 0 1750 B 0 6750 C 0 8500 D 0 4356 E 0 Q6 There are 12 marbles in a bag There are 6 red marbles 4 green marbles and 2 black marbles You reach in and choose 3 marbles without replacement What is the probability that you choose red green and black in this order C 0 0414 A 0 0364 D 0 0612 B 0 0278 E 0 1224

Q1 A coin is tossed and a standard die is rolled How many outcomes are in the sample space A 12 B 8 C 10 D 16 E 72 Q2 The probability of event H is 0 65 According to the Law of Large Numbers which of the following is true A Event H will occur exactly 130 times in 200 trials B Event H will occur approximately 65 of the time for a very large number of trials C Event H will not occur 65 of the time for 130 or fewer trials D Event H will occur 65 of the time for 130 or more trials E The Law of Large Numbers does not tell us anything about the probability of event H Q3 The sample space of a probability process contains events H I J and K The events are mutually exclusive The P H 0 2 P I 0 4 P J 0 3 and P K 0 1 What is the probability of H or I A 0 08 B 0 52 C C 0 0 D 0 6 D 0 6 E 0 9

cantly low nor significantly high is 6 PHL Data Speeds Repeat the preceding exercise using the Verizon data speed of 0 8 Mbps at Philadelphia International Airport PHL of adult females are listed in Data Set 1 Body Data in

A card is drawn from a well shuffled deck of 52 cards Find P drawing an ace or a 9 A standard 52 card deck comprises 13 ranks in each of four suits clubs diamonds hearts and spades Assume each card is equally likely selected 4N 24 N to 13 2 7 26 2 13 IN O 12 13 24 34 Credit to Standard 52 card deck 2022 September 12 In Wikipedia https en wikipedia org wiki Standard 52 card deck 48 34 215

1 5 pts Chief financial officers of U S companies were surveyed about areas in which job applicants make mistakes Here are the areas and the frequency of responses Interview 452 r sum 297 cover letter 141 reference checks 143 interview follow up 113 screening calls 85 a Create a bar chart for this information by hand or with a spreadsheet Make sure everything is labeled b Create a pie chart for this information by hand or with a spreadsheet Make sure everything is labeled Name 2 10 pts Helmets and Injuries The data in the accompanying table is based on data from Helmet Use and Risk of Head Injuries in Alpine Skiers and Snowboarders by Sullheim et al Journal of the American Medical Association Vol 295 No 8 Head Injuries Wore Helmet No Helmet Not Injured 656 2330 96 480 a What is the probability a randomly selected person has a head injury b What is the probability a randomly selected person wore a helmet c What is the probability a randomly selected person had a head injury or wore a helmet d What is the probability a randomly selected person did not wear a helmet and was not injured

to help decide when and where to advertise an electronics repair company decided to pull invoices and tally what types of devices were repaired There were ive devices repaired that month Construct a frequency distribution for the data Fax Laptop Cell Phone Tablet Tablet Cell Phone Fax Devices Repaired Laptop Printer Fax Laptop Cell Phone Laptop Cell Phone Fax Tablet Fax Laptop Cell Phone Laptop

P 14 Prove similarity statements ETX YZ WZ XZ YZ Complete the proof that AXYZ AYWZ Z 1 2 3 Statement WY YZ WZ XZ YZ LZ LZ AXYZ AYWZ X 2 Reason Given Reflexive Property of Cong

For any set A B and C prove that AU B C A B A C

Which of the following statements is false OTwo independent events cannot occur at the same time OTwo complementary events cannot occur at the same time OTwo disjoint events cannot occur at the same time

Test A 49 B 46 a P pass Test A C 34 12 7 b P Test C fail The probabilit 6 The probability is 87 5

Sweaters 200 180 160 140 120 100 80 60 40 20 T O economic growth W 20 40 60 80 100 120 140 160 180 unemployment U X The movement from point U to point W could be caused by apples an improvement in efficiency an advance in production technology

Variable 6 124 Variable 3 4 2 0 30 20 Variable 2 10 0 30 25 20 15 10 5 0 5 5 5 10 15 20 Variable 1 10 Variable 1 10 Variable 1 15 15 25 r 0 9 r 0 4 r 0 8 r 0 99 r 0 0

1 2 0 1 0 1 3 LO a Determine characteristic polynomial of A b Find eigenvalues and corresponding eigenvectors stion 3 A 1

Show Transcribed Text Triangle ABC is defined in the coordinate plane by the points A 1 2 B 4 3 and C 4 0 Under which transformations will the image of triangle ABC be

8 What Happens in Vegas Listed below are prices in dollars for one night at different hotels located on Las Vegas Boulevard the Strip If you decide to stay at one of these hotels what statistic is most relevant other than the measures of center Apart from price identify one other important factor that would affect your choice 212 77 121 104 153 264 195 244

Find the distance from S 1 1 5 to the line L quad x 1 t quad y 3 t quad z 2 t

In a neighborhood 35 of homes have a security system As a security system salesperson you want to know how many houses need to be visited before you find 10 houses without a system 83 62 21 98 72 30 25 94 92 05 12 69 98 63 31 09 99 20 40 12 24 85 37 60 61 08 02 02 69 70 88 37 12 45 98 70 54 64 93 67 80 55 Using the list of random numbers with numbers 00 34 representing households with a system how many households would need to be visited A 12 B 17 C 35

9 On December 5th in Champlain MO the probability of snow is 28 the probability that the maximum temperature for the day will be above zero is 80 and the probability that it will both snow and be above zero is 60 What is the probability that it will snow OR the temperature will be above zero Show your work

If A is a 5 x 5 matrix with det A 3 what is the determinant of 2A 2

Plastic parts produced by an injection molding operation are checked for conformance to specifications Each tool contains 14 cavities in which parts are produced and these parts fall into a conveyor when the press opens An inspector chooses 1 part s from among the 14 at random Two cavities are affected by a temperature malfunction that results in parts that do not conform to specifications Round your answers to four decimal places PRUUPUAN A I Are OSLENDAN 06 07 07 05 25321 Samman 240 000 a What is the probability that the inspector finds exactly one nonconforming part b What is the probability that the inspector finds at least one nonconforming part

Suppose a jar contains 6 red marbles and 39 blue marbles If you reach in the jar and pull out 2 marbles at random at the same time find the probability that both are red

Use the following probabilities to answer the question It may be helpful to sketch a Venn diagram P A 0 51 P B 0 39 and P AandB 0 10 P BA

Which of the following statements is false OTwo complementary events cannot occur at the same time OTwo disjoint events cannot occur at the same time Two independent events cannot occur at the same time

A CBS News poll conducted June 10 and 11 2006 among a nationwide random sample of 651 adults asked those adults about their party affiliation Democrat Republican or none and their opinion of how the US economy was changing getting better getting worse or about the same The results are shown in the table below Republican Democrat none P better better same worse 38 104 44 12 87 137 21 90 118 Express your answers as a decimal and round to the nearest 0 001 in other words type 0 123 not 12 3 or 0 123456 If we randomly select one of the adults who participated in this study compute P affiliated with neither party P better affiliated with neither party P affiliated with neither party better P affiliated with neither party and better

A die is rolled twice What is the probability of showing a 5 on the first roll and an even number on the second roll Your answer is

If we say that f x y 9x 2 y 2 make a drawing of the level curves of f for the values c 0 1 9 also drawing for the sections of the graph of f in the plane x 1 x 0 x 1 y 1 y 0 y 1 and draw the graph of f

a 4 digit numbers 2 A display case has room for 10 statues Find the number of ways 10 statues can be displayed if each number of statues is available a 10 statues b 20 statues b 6 digit numbers 3 Find the number of permutations of the letters in each word a factorial b permutation 4 In a class of 30 students find the number of permutations for each situation a 7 students for the debate team b 25 students for the baseball team c first second and third place in the art show Find the value of each expression a 8C3 10 C4 b c applications 12C3 3C C 10 P4

DEPENDENT EVENTS Use the details about the game to answer the questions below In a board game students draw a number do not replace it and then draw a second number Determine the probability of each event occurring I 6 6 9 1 Drawing an odd number then drawing a 6 7 Drawing a 9 then drawing a number divisible by 1 4 Drawing a 1 then drawing 5 Drawing a prime number a 6 then drawing a composite number A C 4 8 6 64 B Choose the best answer below for question 10 10 Harmony places the letters in the word DECEMBER into a bag A letter will be randomly selected and not replaced Then another letter will be selected What is the probability of Harmony selecting a C and then an E D 2 D 6 2 3 56 2 Drawing a 2 then drawing another 2 18 8 Drawing an even number then drawing 1 3 Drawing a number divisible by 3 then drawing a 1 6 Drawing a 9 then drawing another 9 9 Drawing a 6 then drawing an odd number

A researcher records the number of employees of each of the IT companies in the town of Westmoore The results are summarized in the table Find the class limits of the third class Number of IT Companies Number of Employees 0 499 500 999 1 000 1 499 1 500 1 999 2 000 2 499 A lower limit 1 0UU upper limit 1 500 B lower limit 999 5 upper limit 1 499 5 C lower limit 1 000 upper limit 1 499 D lower limit 999 upper limit 1 500 36 21 10 10

Q3 In an F1 race there will be 20 racers from 10 different teams A fan contemplates the outcome of the upcoming Italian Grand Prix Monza and guesses who will be on the podium top three a If only considering racers on the podium who is first second or third does not matter how many different outcomes are possible b If each outcome in part a is equally likely what is the chance that the three racers he chooses are all on the podium How many different outcomes are possible if considering the first the second and the third

Q2 Calculate the following values a Find out 3 7 and 10 b Find out C30 or 10C3 c Find out P30 or 9P3 d Write down the Excel formula for 7 and C30

Write the polynomial in the form p x d x q x r x You may use synthetic division wherever applicabl p x x5 x 3x 3x 3x 3 d x x 2x 2 Preview

set of numbers x 1 x 0 Graph the set of numbers on the real number line Use the tools to enter your answer A WebAssign NumberLine POD 2 3 5 NC SO Help

Roulette is a casino game that involves players betting on where a ball will land on a spinning wheel An American roulette wheel has 38 numbered slots half of the slots from 1 to 36 are red and the other half are black Slots 0 and 00 are both green Suppose that a player bets 1 on the color red If the ball lands in a red slot the player gets their initial 1 back plus a payout of 1 If the ball doesn t land in a red slot they lose their 1 bet Let X the player s net gain from a 1 bet on a the color red Here is the probability distribution of X Win X net gain 1 18 P X 38 Lose 1 20 38 Calculate the mean of X You may round your answer to the nearest thousandth E X dollars

You are filling an aquarium with starts with 3 gallons of water the sink add water at a rate of 2 5galoons per minute write a linear equation to represent how much water is in the tank after a certain amout of

Draw the unit circle and plot the point P 6 2 Observe there are TWO lines tangent to the circle passing through the point P Answer the questions below with 3 de places of accuracy L1 L2 a The line L is tangent to the unit circle at the point 0 162 0 972 I b The tangent line L has equation y X X 1 029 P c The line L2 is tangent to the unit circle at the point 0 462 d The tangent line L2 has equation y x 0 887

The census bureau for a large country has reported that the country is becoming more diverse The projocted population in milions of a certain minority is modeled by the exponenfial functionh t 37 85 1 027 twheret Ocorresp onds to 2000 and0 sts50 Complete parts a and b below a Estimate in what year the minority s population will double the 2005 populason of43 28milion Use the algebra of logarthms to colve this probiam The minonty s population will double the 2005 population in Round down to the nearest whole number b The projected population in milions of another minority is modeled by the exponential function h 1 11 19 1 032 wheret Ocorresponds to 2000 and 0 s 15 so Estmate in ahat year this minority o population wit double the 2005 population of 13 10million This minority s population wal double the 2005 population in Reund down to the nearest whole number