Probability Questions and Answers

A study reports that 61 of Americans support increased funding for public schools If 3 Americans are chosen at random what is the probability that a All 3 of them support increased funding for public schools b None of the 3 support increased funding for public schools c At least one of the 3 support increased funding for public schools Next Question

Suppose the body mass index BMI of a group of athletes has a population mean of 24 98 and a standard deviation of 4 18 If a random sample of 150 athletes is chosen for a study compute the standard deviation of the sampling distribution of the mean Give your answer to two decimal places Standard deviation of the sampling distribution of the mean

e probability is 0 3 that a traffic fatality involves an intoxicated or alcohol impaired driver or nonoccupant In six traffic fatalities find the probability that the number Y which involve an intoxicated or alcohol impaired driver or nonoccupant is exactly three at least three at most three between two and four inclusive Find and interpret the mean of the random variable Y Obtain the standard deviation of Y The probability that exactly three traffic fatalities involve an intoxicated or alcohol impaired driver or nonoccupant is ound to four decimal places as needed

20 The numbers 1 through 8 are written in separate slips of paper and the slips are placed into a box Then 4 of these slips are drawn at random What is the probability that the drawn slips are 1 2 3 and 4 in that order A 0 01429 B 0 34296 C 0 000595 D 0 01428 2 20

2 It is thought by some researchers that exercise for college students is related to the sex of the student A survey was taken of 470 college students in California that relates their sex to the frequency of exercise per week The results are summarized in the contingency table below Male Female Totals No exercise per week 0 3893 0 4723 0 4720 88 0 4357 72 160 Once or twice per week More than twice per week Totals 76 58 222 248 470 If one of the 470 college students is selected at random what is the probability that the student is a male given that the student exercises more than twice per week Round your answer to 4 decimal places None of the above 85 161 91 149

39 9 of consumers believe that cash will be obsolete in the next 20 years Assume that 6 consumers are randomly selected Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years The probability is Round to three decimal places as needed

t a large high school outside of Chicago there are two students running for class president Ronald and Bo 60 of the students in the school support Bo and the remaining 40 support Ronald If you randomly sampled 12 students what is the probability that more than half of your sample is comprised of Ronald supporters Assume independence between students Note Round to the nearest thousandth

A bag contains 10 marbles Four of them are red three blue two white and one yellow A marble is drawn at random What is the probability that it is not red Be sure to reduce

Select the correct answer from each drop down menu Of the 16 cards drawn from a standard deck of 52 cards experimental probability of drawing a spade is a spade from a standard deck of cards is 5 of the cards are spades Based on the cards that were drawn the and the difference of the experimental and theoretical probabilities of drawing

Select the correct answer from the drop down menu A number cube is biased to land on the number 3 about 50 of the time It is rolled 42 times and the outcomes are recorded The least likely result for the number cube to land on the number 3 is times 25 18 et Next

Suppose a game consists of two steps First you roll a die If you roll a 6 you continue otherwise you lose the game If you rolled a 6 an can continue playing the game the second step is to randomly choose a card from a standard deck of 52 playing cards If you draw face card ie jack queen or king you win

Say that a game consists of two steps First you roll a die If you roll a 1 or a 6 you continue otherwise you lose the game If you rolled a 1 or a 6 and can continue playing the game the second step is to draw a random card from a standard deck of 52 playing cards If you draw an ace or a 6 you win What is the probability that you will win this game 2 39 1 3 8 52

The city of Raleigh has 11200 registered voters There are two candidates for city council in an upcoming election Brown and Feliz The day before the election a telephone poll of 550 randomly selected registered voters was conducted 237 said they d vote for Brown 267 said they d vote for Feliz and 46 were undecided Describe the sample for this survey O All citizens of Raleigh O All registered voters in Raleigh O All registered voters with telephones in Raleigh O The 550 voters surveyed O The 237 voters who said they d vote for Brown O None of the above

All changes An archery target is shown The length of a side of the inner square is 6 ft and the length of a side of the outer square is 11 ft If an arrow hits the target at random what is the probability hits the shaded region Round to the nearest percent 11 ft 6 ft

Edna is fouled hard in an exciting basketball game It is ruled a flagrant foul and the opponent is tossed from the game As a result Edna is allowed to shoot two free throws She is a good shooter and on average makes 82 of her free throws Assuming independence between the 2 free throws what is the probability

Of the 16 cards drawn from a standard deck of 52 cards 5 of the cards are spades Based on the cards that were drawn the and the difference of the experimental and theoretical probabilities of drawing experimental probability of drawing a spade is spade from a standard deck of cards is V 1

You have a bad habit of overpacking On an overnight field trip with the school you packed five shirts and one pair of jeans Two of your shirts are yellow and the other three are black What is the probability you randomly reach into your suitcase and pull out a yellow shirt 100 O 30 O 20 O 60

Parte Part 1 of 2 a Find the probability that both prizes are won by men The winning ticket is not replaced Enter your answer as a fraction or a decimal rour decimal places P both prizes won by men

In a certain Algebra 2 class of 28 students 9 of them play basketball and 17 of them play baseball There are 6 students who play neither sport What is the probability that a student chosen randomly from the class plays both basketball and baseball

There is a 80 chance that a person eats dinner a 70 chance a person eats dessert and a 40 chance the person will eat dinner and dessert Which of the following is true OA Eating dinner and eating dessert are dependent events because P dinner P dessert 0 8 0 7 0 1 which is less than P dinner and dessert 0 4 B Eating dinner and eating dessert are independent events because P dinner P dessert 0 8 0 7 0 56 which is not equal to P dinner and dessert 0 4 O C C Eating dinner and eating dessert are dependent events because P dinner P dessert 0 8 0 7 0 56 which is not equal to P dinner and dessert 0 4 D Eating dinner and eating dessert are independent events because P dinner P dessert 0 8 0 7 0 1 which is less than Pidinner and dessert 0 4

In a study of data derived from a variety of natural phenomena F A Benford formulated an empirical law regarding the frequency of occurrence of the first digit d in a set of numbers Researchers have recognized Benford s law also known as the first digits law as an important tool in data analysis for diverse arenas such as forensic accounting online social networking climate modeling and gene sequencing For specific data sets Benford observed that the frequencies of occurrence of d were approximated by the probability distribution shown in the table d 1 2 3 4 5 6 7 8 9 P d 301 176 125 097 079 067 058 051 046 Use Benford s Law to find P d 5 and P d 2 Express each result as a decimal rounded to three places P d 5

Out of 9 700 college students surveyed 776 responded that they do not eat breakfast What percent of the students not eat breakfast Percent of the students

Tim works for a cell phone company and is testing their new biometric security feature He conducted a test in which 4 000 attempts were made to unlock the phone Of the attempts to unlock the phone 25 were made by someone other than the phone s owner The results of the test are shown in the table Owner Not the Owner Total OA 6 2 OB 8 8 OC Unlocked 2 418 232 2 650 9 6 Did Not Unlock 582 768 1 350 What is the probability that someone who is able to unlock the phone using the biometric security feature is not the owner Total 3 000 1 000 4 000

Suppose the circle graph shows the percent of people in a certain region with the various types of blood If one person in the egion is selected at random use the graph to determine the probability that the person has AB blood The probability is Simplify your answer Question Help AB AB B 2 B A 8 A 3 0 6 O

instructul Skyward bhoney cake pictur Harry surveyed soccer athletes on what drink they preferred during their athletic competition The results are in the following Two Way Frequency Table Gender Gender O 0 36 0 48 Girl Boy Total When converting the above frequency table to a two way relative frequency table what is the value of E O 0 75 Preferred Drinks Powerade 3 9 12 Girl Boy Total Gatorade 5 8 13 Preferred Drinks Powerade B Gatorade A D G tur E Total 8 17 25 H Total U LL

Rodney s Repair Service has a lug nut tightening machine that works well 85 of the time They got a new machine that works well 99 of the time Each machine is used 50 of the time Use Bayes Theorem to find the probability If necessary round your calculations to the nearest thousandths and write your answer as a percent The old machine malfunctioned The old machine will malfunction of the time

Paul needs to randomly select one of his four children to go first in a board game Which simulation tools could he use in this situation two coins a standard deck of cards a spinner divided evenly into 12 sections with three sections each of four different colors a bag containing 12 chips in two different colors with six of each color a six sided number cube

Suppose that Jason recently landed job offers at two companies Company A reports an average salary of 51 500 with a standard deviation of 2 050 Company B reports an average salary of 46 820 with a standard deviation of 5 755 Assume that salaries at each company are normally distributed Jason s goal is to secure a position that pays 55 000 per year What are the z scores for Jason s desired salary at Company A and Company B Please round your answers to two decimal places I Company A z Company B z At which company is Jason more likely to obtain his desired salary of 55 000 per year O Company B because the z score for 55 000 at Company B is greater than the z score for 55 000 at Company A O Company A because the z score for 55 000 at Company A is greater than the z score for 55 000 at Company B O Company B because the z score for 55 000 at Company B is less than the z score for 55 000 at Company A

Suppose a county s recent health report gives a pet allergy prevalence of 0 16 for kids There is a new at home test kit for pet allergies on the market that provides families with a convenient way to test if children have a pet allergy The probability that the test gives a positive result when a child really does not have a pet allergy is 0 04 The probability that the test gives a negative result when a child really does have a pet allergy is 0 15 The tree diagram shows the possible outcomes with the associated probabilities What is the probability of an incorrect test result Give your answer as a decimal precise to two decimal places P incorrect test result Pet allergy status 0 16 0 84 Pet allergy No pet allergy Test result 0 85 0 15 0 04 0 96 Positive Negative Positive Negative

7 The principle of redundancy is used when system reliability is improved through redundant or backup components Assume that a student s alarm clock has a 17 1 daily failure rate Complete parts a through d below a What is the probability that the student s alarm clock will not work on the morning of an important final exam Round to three decimal places as needed b If the student has two such alarm clocks what is the probability that they both fail on the morning of an important final exam Round to five decimal places as needed c What is the probability of not being awakened if the student uses three independent alarm clocks Round to five decimal places as needed d Do the second and third alarm clocks result in greatly improved reliability A Yes because total malfunction would not be impossible but it would be unlikely B Yes because you can always be certain that at least one alarm clock will work C No because total malfunction would still not be unlikely D No because the malfunction of both is equally or more likely than the malfunction of one

3 2 31 According to a study 79 of K 12 schools or districts in a country use digital content such as ebooks audio books and digital textbooks Of these 79 3 out of 10 use digital content as part of their curriculum Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is Round to three decimal places as needed

There are seven white dogs five black dogs six white cats and three black cats What is the probability of randomly selecting a white animal or a dog Use the paperclip button below to attach files

Your college is having a housing lottery The probability that you will get a single room all to yourself next year is 0 2 the probability of getting a double is 0 6 and the probability of getting a triple is 0 2 All of the triples have air conditioning half of the doubles have air conditioning and only 10 of the singles have air conditioning What is the probability that your dorm room next year will have air conditioning

An unusual number cube with 6 sides has the numbers 2 2 4 4 6 and 6 on its faces It is rolled once Match the outcome to its probability 1 P2 or 4 2 P multiple of 2 3 P multiple of 3 4 Plodd prime numbers 0 1 3

A warehouse employs 27 workers on first shift 16 workers on second shift and 14 workers on third shift Eight workers are chosen at random to be interviewed about the work environment Find the probability of choosing exactly two second shift workers and two third shift workers The probability of choosing two second shift workers and two third shift workers is Round to three decimal places as needed

10 points In a class of 30 students 13 have a cat and 10 have a dog There are 4 students who have a cat and a dog What is the probability that a student who does not have a dog has a cat You must draw a two way table on your scratch paper to earn full points for this question The probability that a student does not have a dog but has a cat is kype your answer

Al changes 3 A five question multiple choice quiz has five choices for each answer Use the random number table provided with 0 s representing incorrect answers 1 s representing correct answers to answer the following question What is the probability of correctly guessing at random exactly one correct answer Round your answer to the nearest whole number Random Number Table 10000 11111 01000 10011 01101 10111 10110 11110 11100 11100 11100 10010 01100 11101 10000 00111 10110 11000

A large white canvas 9 x 21 has two triangles painted on it one with a base of 1 and height of 3 and the other with a right triangle with a hypotenuse of 5 and a side of 3 What is the probability of throwing a drop of paint into one of the triangles O 1 9 O 12 O 4 0 O 14

A lottery consists of 36 numbers You must pick the six winning numbers to win What is the chance of you winning Enter your answer as an exact value Type an integer or a simplified fraction

Internet Use in 2000 The following pie chart shows the percentage of the population that used the Internet in 2000 broken down further by family income and based on a survey taken in August 2000 35 000 Internet user 11 35 000 Nonuser 24 35 000 Internet user 35 35 000 Nonuser 30 a Determine the probability that a randomly chosen person was an Internet user given that his or her family income was less than 35 000 Round your answer to two decimal places 0 27 MY NOTES ASK YOUR TEACHER b Based on the data was a person more likely to be an Internet user if his or her family income was less than 35 000 or 35 000 or more Support your answer by citing the relevant conditional probabilities Round your answers to two decimal pla By comparing P Internet user 35 000 with P Internet user 2 35 000 it can be determined a person is more likely to be an Internet user if his or her family income was less than 35 000

A company has 9000 arrivals of Internet traffic over a period of 21 060 thousandths of a minute Let the random variable x represent the number of such Internet e traffic arrivals in one thousandth of a minute It appears that these Internet arrivals have a Poisson distribution If we want to use the formula P x find the probability of exactly 4 arrivals in one thousandth of a minute what are the values of x and e that would be used in that formula P Round to three decimal places as needed to

Type the correct answer in each box Spell all words correctly and use numerals instead of words for numbers The coach of a soccer team is determining which of the team s three goalies will play in today s game The weather forecast gives a 100 chance of rain and the team needs to win or tie to stay in the tournament The coach compiled data on goalie performance during rain given in the table below April Tony Conner April Tony Based on the data given calculate the win or tie percentage in rain for each goalie Conner 96 96 Games Won in Rain Games Tied in Rain Games Lost in Rain 6 3 6 5 7 4 4 10 6

A single serving coffee machine is programmed to dispense 8 ounces of coffee per serving Occasionally the machine will start to overfill or underfill cups of coffee and require recalibration According to the company the coffee machine requires recalibration if it overfills or underfills cups of coffee by 1 or more ounces Determine the probability that a randomly selected cup of coffee was underfilled or overfilled by more than 1 ounces Assume the distribution of the amounts of all coffee dispensed by the machine are normally distributed with a mean of 8 ounces and a standard deviation of 1 75 ounces The probability that a randomly selected cup of coffee is overfilled or underfilled by 1 ounces is

Instead of using the values 1 2 3 4 5 6 on dice suppose a pair of dice have the following 1 2 2 3 3 4 on one die and 1 3 4 5 6 8 on the other Find the probability of rolling a sum of 7 with these dice Be sure to reduce

Hal earns a B on 75 of his tests He divides a spinner into 12 equal spaces to model the grades he earns on his tests with nine of the spaces representing a B Which statement about his model is true OA His model can be improved the most by using eight of the spaces to represent a B B His model can be improved the most by using every third space on the spinner to represent a B OC His model cannot be improved OD His model can be improved the most by dividing the spinner into 15 equal spaces

Based on probability and if it is appropriate for a decision to be left up to chance choose every situation that is both statistically fair an morally fair Situation 1 Situation 2 A high school student is deciding whether to first clean his room or do his homework He decides by picking a tile at random from a bag of lettered tiles If he picks a consonant he will clean his room and if he picks a vowel he will do his homework Situation 3 There are four candidates eligible for a vacancy at a company Ignoring qualifications and experience the recruitment manager decides which candidate to hire by writing their names on pieces of paper shuffling the papers and drawing one at random Five cousins are deciding which board game to play They each write their preferred game on a different section of a spinner that has five equally sized sections They spin the spinner and will play the game written on the section where the spinner lands To determine who can choose the spot for a picnic Kate picks a tile at random Situation 4 from a collection of five tiles numbered 2 through 6 Kate chooses the spot if she picks a prime number and Charles chooses if Kate picks a composite number Five roommates all want to attend an event but they only have four invites To decide who will attend they shuffle a set of five cards consisting of four aces and a king Each roommate is randomly dealt a card The ones dealt an ace will attend Situation 5 the event

Convert the two way table to a relative frequency table Has siblings Does not have siblings Rides the bus to school Does not ride the bus to school Has siblings Does not have siblings Has siblings 122 10 Does not have siblings Rides the bus to school Value here Does not ride the bus to school Value here Rides the bus to school Value here Does not ride the bus to school Value here 64 4 1 0 32 2 0 02 3 0 25 4 0 10 5 0 05 6 0 45 7 0 75 8 0 61

0 A survey asks 1500 workers Has the economy forced you to reduce the amount of vacation you plan to take this year Forty one percent of those surveyed say they are reducing the amount of vacation Twenty workers participating in the survey are randomly selected The random variable represents the number of workers who are reducing the amount of vacation Decide whether the experiment is a binomial experiment If it is identify a success specify the values of n p and q and list the possible values of the random variable x spolity and value 1 TELL CHRIVE USUW aitu sirmarry die DASS I your VILE A n 20 OB This is not a binomial experiment Specify the value of p Select the correct choice below and fill in any answer boxes in your choice OA p B This is not a binomial experiment Type an integer or a decimal

The positions on a lacrosse team are called defenders D midfielders M and attackers A One player is chosen at random to lead the team in exercises before each game The letters MDD mean that a midfielder was chosen at the first game and a defender was chosen at the next two games The list of all possible outcomes is shown where each outcome has equal probability of occurring AAA AMA ADA MAA MMA MDA AAM AMM ADM MAM MMM MDM AAD AMD ADD MAD MMD MDD What is the probability that a defender is chosen at least once given that a midfielder is chosen at the first game O A O B 19 DAA DMA DDA DAM DMM DDM DAD DMD DDD 113

4 Consider the following scenarios using two strings Part A Is it possible to construct a square with the two strings Explain your answer Part B Is it possible to construct a rectangle with the two strings Explain your answer