Probability Questions and Answers

A restaurant offers dinner specials as shown in the menu You can order one item from each catego 12 Appetizer chips dip wings 08 stuffed mushrooms Main Course Beverage Dessert burger salad pasta How many possible choices of the dinner special are there kabob soda juice cake cookie ice cream

There are four red five blue and eight green balls in a bag The balls are identical except for color If three balls are randomly selected what is the probability that they are all blue O O OF

The two way table shows if campers can or can t swim Boys Girls Total Can Swim Can t Swim Total 28 32 60 22 18 40 50 50 100 One girl will randomly be chosen What is the experimental probability that she cannot swim

31 Santia is considering a vacation and has obtained high temperature data from the last two we for Miami and Los Angeles Miami Los Angeles 76 81 74 75 83 63 62 83 85 65 72 73 83 67 69 60 87 65 64 66 80 65 64 76 80 65 61 Which location has the least variability in temperatures Explain how you arrived at your answer 32 S

b What is the probability that the sample mean income is between 38 and 46 5 points

5 Big babies A public health organization reports that 20 of baby boys 6 8 months old in the United States weigh more than 20 pounds A sample of 17 babies is studied Round the answers to three decimal places a What is the probability that exactly 8 of them weigh more than 20 pounds 2 points h What is the probability that more than 6 weigh more than 20 pounds

Chapter 3 3 A population has mean 30 and standard deviation o 7 a Find the Z score for a population value of 9 2 points b Find the z score for a population value of 51 c What number has a z score of 2 3 2 points 2 points

10 points Lottery Every day Jorge buys a lottery ticket Each ticket has a probability of 0 2 of winning a prize After five days what is the probability that Jorge has won at least one prize Round your answer to four decimal places

Given the following events A likes spicy food B uses hot sauce How should you analyze the conditional probability P A B OFirst consider the people that use hot sauce then find the probability that they like spicy food O First consider the people that like spicy food then find the probability that they use hot sauce O First find the probability that someone uses hot sauce then find the probability that someone likes spic O First find the probability that someone likes spicy food then find the probability that they use hot sauce

At a factory the probability that a pair of sunglasses will have a scratch on the lens is 0 03 A manager randomly selects a pair of sunglasses to inspect at irregular intervals What is the probability that a manager will encounter a scratched pair of sunglasses on the fourth inspected pair of the day 0 274 0 120 0 885 0 312 Jy

For a flash drive there is a memory capacity of 2 GB 4 GB 8 GB and 16 GB and there are five colors What is the of selecting a 4 GB flash drive assuming that the probabilities of selection are the same for all options probability O 15 0

Suppose you have a bag containing 5 white marbles 8 black marbles 4 red marbles and 9 green marbles You draw a single marble record the color and then place the marble back into the bag You do this 10 times in total After the final time you count your observations and see that you drew a black marble 3 times Using what you know about theoretical probabilities was this likely to occur Explain

Five thousand tickets are sold at 1 each for a charity raffle Tickets are to be drawn at random and monetary prizes awarded as follows 1 prize of 900 3 prizes of 100 5 prizes of 50 and 20 prizes of 5 What is the expected value of this raffle if you buy 1 ticket Let X be the random variable for the amount won on a single raffle ticket EX dollars Round to the nearest cent as needed KIIB

Arrange these events in the order in which they occur in the story Rue is killed FIRST SECOND Thresh allows Katniss to live THIRD Katniss finds Peeta FOURTH Katniss loses hearing in one

7 Netflix has changed its pricing model to restrict users from sharing their account It now has a base subscription cost of 5 per month and an additional fee of 3 for every additional IP address linked to the account a Write a linear function that describes the pricing model Clearly define all variables b How much will it cost to have 7 additional IP addresses on your account If you have to pay 25 a month to Netflix how many IP addresses would be G linked to your account

2 Find the three arithmetic means between 1 and 69 1 69 O 14 38 49 O 23 40 46 O 18 35 52 O 17 37 54 O None of these are correct

ANFL National Football League study was conducted to investigate the relationship between total team salary x in millions of dollars and the number of wins y out of 16 regular season games The following regression equation was obtained y 1 783 0 0621 a Which is the correct interpretation of the slope of the line For every 1 million more in team salary the number of wins increases by 0 062 O For every 0 062 million more in team salary the number of wins decreases by 1 783 For every 1 783 million more in team salary the number of wins decreases by 0 062 For every 1 million more in team salary the number of wins increases by 1 783 b A team spent 60 million on team salary and its residual was 1 503 How many games did they actually win

1 2 A jar contains 15 red 25 blue 35 orange and 45 pink marbles A marble is drawn at random P pink 3 5 6 4 A jar contains 9 orange and 15 white marbles A marble is drawn at random P white 7 8 9 one marble is chosen what is the probability that it will be les in a bag and 25 of them are green If green C A jar contains 12 black 35 blue 45 yellow and 34 green marbles A marble is drawn at random P not green des A number from 21 to 41 is drawn at random P a prime number estive You roll a die numbered from 1 to 6 P an odd number 3 A number from 55 to 75 is drawn at random P a number divisible by 5 lazdub to LAURENT SOILLES uz vus to s brus hat 10 93 21 W hom aludongda has go nie woln hat You roll a die numbered from 1 to 6 aud wally a grilling to w P not 4 SAW a nito u the a rol line abward oed gulasy to undong all a Womit hohe You roll a die numbered from 1 to 6 P Number 2 and 4 In vihdoing grad nic sha

Next question You can retry this question below Suppose the true proportion of voters in the county who support a restaurant tax is 0 35 Consider the sampling distribution for the proportion of supporters with sample size n 191 What is the mean of this distribution 0 35 0 What is the standard deviation of this distribution Round to 4 decimal places Question Help Message instructor Post to forum

Suppose a university accepts 70 of the students who apply The probability of being accepted and being given on campus housing is 60 What is the probability that you will get on campus housing given that you are accepted 0 86 O 0 42 O 0 65 O 0 80

1 When two births are randomly selected the sample space for genders is bb bg gb and gg Assume that those four outcomes are equally likely Construct a table that describes the sampling distribution of the sample proportion of girls from two births Does the mean of the sample proportions equal the proportion of girls in two births Does the result suggest that a sample proportion is 1 an unbiased estimator of a population proportion For the entire population assume the probability of having a boy is the probability of having a girl is and this is not affected by how many boys or girls have previously been born 2 2 Determine the probabilities of each sample proportion Sample proportion of girls Does the mean of the sample proportions equal the proportion of girls in two births 1 OA Yes both the mean of the sample proportions and the population proportion are 2 OB No the mean of the sample proportions and the population proportion are not equal OC Yes both the mean of the sample proportions and the population proportion are 1 4 1 OD Yes both the mean of the sample proportions and the population proportion are Probability Type integers or simplified fractions

Based on a smartphone survey assume that 47 of adults with smartphones use them in theaters In a separate survey of 300 adults with smartphones it is found that 140 use them in theaters a If the 47 rate is correct find the probability of getting 140 or fewer smartphone owners who use them in theaters b Is the result of 140 significantly low O a If the 47 rate is correct the probability of getting 140 or fewer smartphone owners who use them in theaters is Round to four decimal places as needed b Is the result of 140 significantly low because the probability of this event is than the probability cutoff that corresponds to a significant event which is

3 Is a heart rate above 80 bpm independent of being below 10 000 ft How do you know Tell me with the math rule for independence

4 If the P A 0 4 the P B 0 3 and the P A and B 0 2 what is the P A or B addition rule

A grocery store records the type of eggs purchased by every customer during the month of August Using the collected data the manager developed the following probability model Egg type Small Medium Large Jumbo Probability 0 14 0 28 0 45 Directions 1 What is the probability a randomly selected customer buys jumbo eggs 2 What is the probability a randomly selected customer buys a small or medium egg

of Carol was sitting in her parked car when it was hit by a driver operating an 50 uninsured motor vehicle As a result Carol sustained injuries as did the driver of the other car Carol s Uninsured Motorists Coverage is available to provide coverage to whom Carol only the driver of the uninsured vehicle Carol and the driver of the uninsured vehicle no one since Carol s vehicle was parked For 2 points

7 Perform the indicated goodness of fit test In studying the responses to a multiple choice test question the following sample data were obtained At the 0 05 significance level test the claim that the responses occur with the same frequency Determine the test statistic and critical value Response A B C D E Frequency 12 15 16 18 19 Test statistic x 1 875 Critical value x 9 488 Test statistic x 1 875 Critical value x 11 071 O Test statistic x 9 488 Critical value x 11 071 O Test statistic x 0 178 Critical value x 9 488

3 Simon constructed an online survey for campers to determine which sports were the most popular at his sports camp Simon is almost finished creating the preference schedule shown Using a Borda count which of the following is the correct point amount for swimming number of votes 1st 2nd 3rd 150 15 100 30 50 45 O100 45 50 15 soccer swimming baseball baseball swimming soccer

Do Generation X and Boomers differ in how they use credit cards A sample of 1 000 Generation X and 1 000 Boomers revealed the results in the accompanying table a If a respondent selected is a member of Generation X what is the probability that he or she pays the full amount each month b If a respondent selected is a Boomer what is the probability that he or she pays the full amount each month c Is payment each month independent of generation Click the icon to view the table a If a respondent selected is a member of Generation X what is the probability that he or she pays the full amount each month Round to three decimal places as needed

Use the contingency table below to find the probability of the following events a A B b AB c A B d Are events A and B independent a P A B 0 03 Round to two decimal places as needed A A B 10 20 B 20 50

Suppose that the random variables Z Z and Z3 have the sample cor relation matrix R 1 1 5 1 4 1 5 1 1 3 1 4 1 3 1 i Find the exact one factor solution for the correlation matrix R and write down the factor loadings and specific variances for the one factor model 9 ii Use the principal component method to calculate the factor loadings and specific variances of the two factor solution for R 9

7 P A 0 25 P B 0 35 P A and B A 0 2 B 0 5 C D 0 0875 0 135

1 Solve for the following quantities given the matrices below L E X 3 0 5 2 j3 In j3 j123 1 5 1 Im 0 3j 3 2 j 5 5 3 5 j sinj 0 2 j0 5 1 3 5 4 11 7 1 5 9 1 LEX 2 LT XT 3 A23 of L M31 of E A12 of X 4 El use Laplace Cofactor 5 IX use Pivotal Method j 3 j

In a school 60 of the students have brown eyes Find the experimental probability that in a group of 4 students at least one of them has brown eyes The problem has been simulated by generating random numbers The digits 0 9 were used Let numbers 2 4 and 8 represent the 30 of students with brown eyes A sample of 20 random numbers is shown 13 20 6075 7918 7910 2546 1390 1230 2386 0793 7359 3048 5621 9732 2816 6147 5978 9436 3806 5971 6173 1430 0 65 Experimental Probability

1 10 points Let x be a number of card that a randomly selected auto mechanic repaires in a given day The following table lists the probability distribution of x 2 x P x a Find the value of the missing probability b Find the mean and standard deviation of the random variable x c Find P x 4 3 0 1 4 0 3 5 0 2 6 0 1

a What is the equation for the line of best fit b Draw the line of best fit on the following scatterplot 35 30 25 20 15 10 2 1 5 y 5 S 1 GARAGE 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

X y 2 1044 1430 APA Use linear regression to find the equation for the linear function that best to two decimal places You y 678x 91 3 LETALONCES 3 4 5 6 1939 2456 3398 4519 DEEREAN ETT LEHET GENENAUS LOKE www

0 1 2 3 A survey of 125 students yields the following data for the number of classes they took in the Spring Number of classes taken Frequency of students responding 4 5 6 4 8 12 36 29 24 12 What probability that a randomly chosen student from the survey was taking at most 2 classes Write your answer as decimal rounded to three places

A 2 According to the Venn Diagram above P A P B Select Select P A B P A B 1 Select Select 4 V 3 B

Construction company A is determining whether it should submit a bid for a new shopping center In the past their main competitor construction company B has submitted bids 70 of the time company B does not bid on a job the probability that company A will get the job is 0 20 If company B bids on a job the probability that company A will get the job is 0 15 a If company A gets the job what is the probability that company B did not bid b What is the probability that company A will get the job a If company A gets the job what is the probability that company B did not bid Round to three decimal places as needed CCIDIS

A lock on a bank vault consists of three dials each with 50 positions In order for the vault to open each of the three dials must be in the correct positi a How many different possible dial combinations are there for this lock b What is the probability that if you randomly select a position on each dial you will be able to open the bank vault C n Explain why dial combinations are not mathematical combinations expressed by the equation Cx x n x poccible dial combinations for this lock GEXEM

A daily lottery is conducted in which 4 winning numbers are selected out of 39 numbers without duplication How many different combinations of winning numbers are possible There are different combinations of winning numbers Type a whole number

4 43 Assume that a randomly selected subject is given a bone density test Those test scores are normally distributed with a mean of 0 and a standard deviation of 1 Draw a graph and find the probability of a bone density test score greater than 0 69 Sketch the region Choose the correct graph below OA 0 69 The probability is OB 0 69 0 69 OD A 0 69 0 69

Thirty two people were chosen at random from employees of a large company Their commute times in hours were recorded in a table shown on the right Construct a frequency table using a class interval width of 0 2 starting at 0 15 Class Interval Frequency 0 15 0 35 0 35 0 55 0 55 0 75 0 75 0 95 0 95 1 15 1 15 1 35 1 35 1 55 Which histogram is representative of the above data OA 16 124 84 43 Frequency 55 95 1 35 OB 16 13522 Frequency 55 95 135 Oc 0 4 0 9 0 3 05 07 13 11 07 06 05 08 11 09 02 05 10 09 10 07 02 08 11 07 11 0 5 12 07 06 10 08 05 09

6 76 Texting While Driving According to a Pew poll in 2012 58 of high school seniors admit to texting while driving Assume that we randomly sample two seniors of driving age a If a senior has texted while driving record Y if not record N List all possible sequences of Y and N b For each sequence find by hand the probability that it will occur assuming each outcome is independent c What is the probability that neither of the two randomly selected high school seniors has texted d What is the probability that exactly one out of the two seniors has texted e What is the probability that both have texted

6 75 Drunk Walking You may have heard that drunk driving is dangerous but what about drunk walking According to federal information reported in the Ventura County Star on August 6 2013 50 of the pedestrians killed in the United States had a blood alcohol level of 0 08 or higher Assume that two randomly selected pedestrians who were killed are studied a If the pedestrian was drunk had a blood alcohol level of 0 08 or higher we will record a D and if the pedestrian was not drunk we will record an N List all possible sequences of D and N b For each sequence find the probability that it will occur by assuming independence c What is the probability that neither of the two pedestrians was drunk d What is the probability that exactly one out of two independent pedestrians was drunk e What is the probability that both were drunk

If np 5 and nq 5 estimate P fewer than 4 with n 14 and p 0 5 by using the normal distribution as an approximation to the binomial distribution If np 5 or nq 5 then state that the normal approximation is not suitable Select the correct choice below and if necessary fill in the answer box to complete your choice A P fewer than 4 Round to four decimal places as needed

Recall the sample space for rolling an eight sided dice and flipping a coi H1 H2 H3 H4 H5 H6 H7 H8 T1 T2 T3 T4 T5 T6 T7 T8 Directions Determine the following probability P H Number 7

Recall from the previous practice the question where a group of community members responded to the question Should our town build new high school The following two way table can be used to describe the responses Male Yes Total 119 Female 154 273 No 116 114 230 No opinion Total 6 6 12 241 274 515 Directions 1 Determine the probability for the following problem 2 Interpret the probability P Female No Opinion

peop living at altitudes above and below 10 000 feet Elevation Below 80 bpm Above 10 000 ft 3 Below 10 000 ft 16 total 19 esting heart rate in beats per minute bpm for 50 Above 80 bpm 19 12 31 total 22 28 50 1 What is the probability that a person surveyed selected at random has a heart rate above 80 bpm Find P Above 80 bpm 2 Given a person below 10 000 ft is selected what is the probability they have a heart rate above 80 bpm Find P Above 80 bpm Below 10 000 ft 3 Is a heart rate above 80 bpm independent of being below 10 000 ft How do you know Tell me with the math rule for independence