Probability Questions and Answers

According to the New York State Board of Law Examiners approximately 68 of people taking the New York Bar Exam passed the exam Use this information to find the following probabilities Round solutions to four decimal places if necessary 1 If 10 people who have taken the New York Bar Exam are randomly selected what is the probability that at least 75 have passed Round your answer to 4 decimal places P p 0 75 2 If 48 people who have taken the New York Bar Exam are randomly selected what is the probability that at least 75 have passed Round your answer to 4 decimal places P 0 75 3 Why did the probability decrease The probability decreased since the sample size decreased resulting in a wider distribution which increased the area of the right tail The probability decreased since the sample size increased resulting in a narrower distribution which reduced the area of the right tail

According to a recent Gallup Poll 77 of Americans report that they are better off financially today than they were a year ago Let p be the proportion of people in a random sample of 341 Americans that say that they are better off financially today than they were a year ago Determine the following probabilities Round solutions to four decimal places if necessary Find the probability that in a random sample of 341 Americans less than 72 say they are better off financially today than they were a year ago P p 0 72 Find the probability that in a random sample of 341 Americans between 69 and 75 say they are better off financially today than they were a year ago P 0 69 p 0 75

There are a total of 19 660 IRSC students 71 of which are under the age of 23 In a random sample of 363 students 75 are found to be under the age of 23 Determine how many students in the population and the sample respectively are under the age of 23 Round solutions to the nearest whole number if necessary IRSC students are under the age of 23 students in the random sample of 363 IRSC students are under the age of 23

The distribution of all registered nurses salaries on the Treasure Coast is known to be normally distributed with a mean of 53 150 and a standard deviation of 625 Use this information to determine the following two probabilities Round solutions to four decimal places if necessary Find the probability that a single randomly selected nurse s salary is greater than 53 181 P x 53 181 Find the probability that a random sample of 86 nurses have a mean salary greater than 53 181 P 53 181

A population of values has a normal distribution with 193 3 and o 7 3 You intend to draw a random sample of size n 17 Determine the mean and standard deviation of the sampling distribution of Round solutions to four decimal places if necessary What is the mean of the sampling distribution of What is the standard deviation of the sampling distribution of OF

are outliers on one end of the distribution True False Question 43 What limitations of the mean does the median account for O The influence of modal scores O The influence of multimodal distributions O None of the above 2 pts

According to Masterfoods the company that manufactures M M s 12 of peanut M M s are brown 15 are yellow 12 are red 23 are blue 23 are orange and 15 are green Round all answers to 3 places after the decimal point if necessary a Compute the probability that a randomly selected peanut M M is not green 17 P not green 20 b Compute the probability that a randomly selected peanut M M is red or brown 6 P red or brown 25 c Compute the probability that three randomly selected peanut M M s are all brown P all brown 3 25 d If you randomly select two peanut M M s compute that probability that neither of them are yellow P neither are yellow e If you randomly select two peanut M M s compute that probability that at least one of them is yellow

Taylor got a box of 24 assorted chocolates as a gift The box contains 15 milk chocolates 6 dark chocolates and 3 toffees but they are all individually wrapped so she doesn t know which candy is which kind Dark Chocolate is Taylor s favorite If she eats 2 candies today what is the probability that a Both of the candies are dark chocolate b Neither of the candies are dark chocolate c At least one of the candies is dark chocolate For all of the above round to three decimal places

Stephen buys a bag of cookies that contains 9 chocolate chip cookies 8 peanut butter cookies 4 sugar cookies and 8 oatmeal cookies What is the probability that Stephen reaches in the bag and randomly selects a sugar cookie from the ba eats it then reaches back in the bag and randomly selects a chocolate chip cookie

A factory received a shipment of 47 bolts and the vendor who sold the items knows there are 6 bolts in the shipment that are defective Before the receiving foreman accepts the delivery he samples the shipment and if too many of the bolts in the sample are defective he will refuse the shipment For each of the following give your responses as reduced fractions If a sample of 6 bolts is selected find the probability that all in the sample are defective If a sample of 6 bolts is selected find the probability that none in the sample are defective

Courtney pulls out her famous bag o marbles As everyone knows there are 7 red 10 white and 13 blue marbles in her bag a What is the probability that if she pulls one marble it is white b What is the probability that if she pulls two marbles with replacement they are red and then blue c What is the probability that if she pulls three marbles without replacement they are red then white and then blue For all of the above you may enter an answer or a calculation that leads to an answer no approximations

Dante has a bag of marbles with 3 blue marbles 1 white marbles and 2 red marbles Find the following probabilities of Dante drawing the given marbles from the bag if the first marble s is are not returned to the bag after they are drawn Give your answer as a reduced fraction a A Blue then a red b A red then a white c A Blue then a Blue then 2 Blue

You pick 3 cards from a deck without replacing the card each time before picking the next card What is the probability that all 3 cards are Jacks Leave your answer as a fraction

Find dy da dy for y Question Help In 2x 3 10e F 16

12 a Prove that one of the primes that divides a number of the form 4n 3 where n is any natural number include 0 among these here must itself have the form 4k 3 where k is any natural number k

A coin is tossed twice Let E be the event the first toss shows heads and F the event the second toss shows heads a Are the events E and Findependent Input Yes or No b Find the probability of showing heads on both tosses Write your answer as a reduced fraction Answer

If the odds for a certain event are 3 to 13 what is the probability of the event occuring Write your answer as a simplified fraction

Suppose the probability of an event is 34 37 What are the odds for the event happening to What are the odds against the event happening to

Probability Intersection of Independent Events Determine the following probabilities Enter your final answers as reduced fractions Two coins are flipped Find the probability that the first coin land on tails and the second coin lands on heads Two cards are drawn from a deck of 52 cards The first card is replaced before drawing the second card Find the probability that the first card is red and the second card is a 3 A single digit between 0 and 9 is randomly chosen and a single letter from A to Z is randomly chosen Find the probability that the number is 7 and the letter is a vowel Two dice are rolled Find the probability that first die lands on an odd number and the second die is less than 5

Which of the following statements are true Mark all that apply If the odds for an event are 3 to 5 then the odds against that event are 5 to 3 If the Expected Value of a game is 1 we say that it is a fair game The probability of an event that is certain is 1 Expected Value is the actual gain or loss each time an event takes place The probability of an impossible event is 0 If P A is the probability that event A will occur the probability event A will not occur is P A P A Expected Volvo in the evergo gain or loss of an event if the procedure is repeated many time

An experienced teacher writes an exam so that on average about 5 of students will earn an A grade If she has 50 students in her class and their performance is independent what is the probability that at least one student gets an A

In a drawer there are 13 pairs of socks 5 of which are white and 10 t shirts 6 of which are white If you randomly select one pair of socks and one t shirt what is the probability that both are white Express your answer as a reduced fraction

During a basketball game Abraham is shooting two free throws He makes 95 of his free throws Assuming that his free throws are independent events find the percent chance that he Note Do not round your answers is in the groove and makes both free throws makes the first and then misses the second misses the first and then makes the second struggles and misses both of his free throws What is the sum of these four answers at a a

A die is rolled twice What is the probability that a n 1 is rolled on the first roll and an even number on the second roll The probability of rolling a n 1 on the first roll and an even number on the second roll is

1 Suppose the weather forecaster says the probability of rain tomorrow is 3 Find the probability of no rain tomorrow 2 It has been estimated that 72 7 of alcoholics need professional help to stop drinking What is the probability that a random alcoholic can kick the habit without professional help 3 A marble is drawn at random from a box containing 3 yellow 4 white and 8 blue marbles Find the probability of drawing b a a yellow marble a blue marble d a white or blue marble

Experts calculate the probability of a particular horse winning the Kentucky Derby to be P win 0 55 What is the probability in decimal form that the horse will not win the race P not win What are the odds against the horse winning the race Simplify your answers to

TV Game Show In Exercises 19 22 a television game show has five doors of which the contestant nuust pick two Be hind two of the doors are expensive cars and behind the other three doors are consolation prizes The contestant gets to keep the items behind the two doors she selects Determine the probability that the contestant wins 19 no cars 20 both cars 21 at least one car 22 exactly one car

Question 19 1 point Find the indicated probability 80 of U S drivers over the age of 30 ha have also been in an accident while behin What is the probability that a randomly se had a speeding ticket and also been in an

Question 17 1 point Find the indicated probability sempt 1 Statistics show that about 42 of Americans vote If three Americans are randomly selected what is voted in the previous national election 0 42 0 17

estion 16 1 point ind the indicated probability survey of American women who were asked to name t he following results 18 said blue 19 said red 18 4 said black and the rest named another color you pick a survey participant at random what is the pr olor is yellow or black 0 12 0 26 2014

Now change the setting Replace warbles after each draw to No This means that this time we take the first marble out and keep it out while we choose the second marble Two Marbles What is the sample space for drawing two marbles List the outcomes in the same order as listed in the Gizmo Use a comma to separate the outcomes Do not use any spaces S Two Green Marbles What is the probability of drawing a green and then a green marble P G and G P G P G G of green marbles of green marbles after first drau of marbles of marbles after first draw 0 A probability of O means that the event occur Why can t we draw a green and then another green marble Click here for answer Is P G P G G Are the events independent or dependent Blue and Green Marbles What is the probability of drawing a blue marble and then a green marble P B and G P B P GB

R R RR Y Y Simple Event Fig 6 Venn diagram with four circles containing four red marbles three green marbles two yellow marbles and one blue marble respectively G Enter fractions in reduced form using a for the fraction bar Do not use any spaces in your answer except for the Outcome of Interest R B BAG OF MARBLES X G G G y B Outcome of Interest Choose a marble that is not green Choose a marble that is not red Choose a marble that is not blue Choose a marble that is not yellow 1 P x where x is the P x wher probability is the sim event of choosing the color 1 1 10 1 1 1 100 1 1 5 P G 7 10 P R P B 9 10 x P Y 9

answer 12 2023 There is one green marble and two blue marbles in the bag We chose the green marble on the first draw and we put it aside Now there are 2 blue marbles left in the bag There are no more green marbles to choose so drawing a green marble on the second draw is impossible Is P G P G G no Are the events independent or dependent dependent Blue and Green Marbles What is the probability of drawing a blue marble and then a green marble P B and G P B P GB 1 3 1 3 216 Is P G P G B no Are the events independent or id 6

Suppose a jar contains 10 red marbles and 17 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

A medical testing laboratory saves money by combining blood samples for tests The combined sample tests positive if at least one person is infected In a given test blood samples from 6 randomly selected people are combined What is the probability that the combined sample tests positive It has been determined that one randomly selected person has a 0 0456 chance of testing positive Round your result to 3 significant figures Express the probability as a decimal not as a percent

An elevator has a safety limit that should not exceed 10 people or 1950 lbs When designing elevators a worst case scenario involves having 10 male passengers We know that the weights of men are normally distributed with u 182 9 lb and a 40 8 lb What is the probability that 10 randomly selected men would have a mean weight greater than 195 lbs Does the elevator seem to be designed with appropriate weight limits Justify your response Please write out your calculations on your own piece of paper Your calculations should include the formula used all the variables plugged into the formula and the solution You may type your complete sentence answer and answers to any follow up questions in the text box below Then proceed to the next problem You will be sending a picture of this work to me through email immediately after the exam is over

The Centers for Disease Control and Prevention CDC is working hard to keep the American public safe Suppose the rate of infection for a new disease which has no cure or vaccine is 14 8 Find the mean and standard deviation for the number of people infected with this new disease among 2600 people For full credit please type out your calculations in the space below Round your answer to the nearest tenth Remember to include your units

Assume that SAT scores are normally distributed with mean 1518 and a 325 If 18 SAT scores are randomly selected find the probability that they have a mean greater than 1350 No need to round your answer Express the probability as a decimal not as a percent

4 Reverse In Qwirkle you draw a tiles out of a bag You are told that the odds in favor of drawing a purple diamond are 1 12 the odds against drawing a circle of any color are 5 2 and the odds in favor of drawing a yellow tile are 3 7 Find the probability of drawing a purple diamond Find the probability of drawing a circle tile Find the probability of not drawing a yellow tile

You have a drawer with 30 pairs of socks of various colors and lengths see table You draw a single pair of socks out of the drawer Length White Short 8 Long 3 Blue Red 4 6 Find the odds in favor of getting a pair of short white socks Find the odds against getting a pair of long socks that are not blue 3 6 6

2 Compare the two climogra or B on the right represent a location at 61 C North latitude Explain your response in at least one sentence Precipitation cm Climograph A 400 18 0 36 0 340 320 30 0 280 26 0 240 220 200 18 0 16 0 14 0 12 0 100 80 6 0 4 0 20 00 212 8 e 20 BA 40 Temperature o 288 40 0 30 0 36 0 34 0 32 0 30 0 28 0 26 0 34 0 22 0 200 18 0 16 0 140 12 0 NOO 80 6 0 4 0 20 D 2 Precipitation cm Climograph B Month Figure 9 4 Climograph Examples A on left and B on right Month 146 99 32 ZARRE Y 20 24 20 16 12 OY 16 20 24 Temperature C

The next step to create the example climograph is to plot the temperature data from Table 9 1 We have used an orange line to represent average monthly temperature as shown in Figure 9 3 Note the orange color is arbitrary climographs may show temperature in red or as another color Precipitation cm 400 38 0 360 340 320 30 0 28 0 36 0 240 22 0 200 IRO 16 0 14 0 120 100 8 D 6 0 40 20 60 J Month SOND 32 24 20 16 12 12 16 20 24 Temperature C Figure 9 3 Climograph with Precipitation and Temperature Plotted 145 1 Refer to Figure 9 3 How does the climograph help us understand the location s climate Create a list of what you can determine from the climograph Here are two questions to help you write your response does the location s temperature fluctuate or is it within about a 15 C temperature range throughout the year When is the rainy season This is when precipitation levels increase

You roll two 3 sided dice and record the results Find the odds in favor of getting a total of 3 or more Find the odds against getting two even numbers

Let s eat A fast food restaurant chain has 599 outlets in the Unite presents the number of restaurants in each category A restaurant four decimal places Population of City Under 50 000

What is the probability of obtaining eight heads in a row when tipping a coin interpret this probability REED The probability of obtaining eight heads in a row when flipping a coin is Round to five decimal places as needed Interpret this probability Consider the event of a coin being fipped eight times If that event is repeated ten thousand different times it is expected that the event would result in eight heads about s Round to the nearest whole number as needed

Xenia s coin H H H H T T T T Yolanda s coin 9 Game 1 A player wine if she is the only one to toss heada Is this a fair game Answer choices Yes Each player s probability of winning is Yes Each player s probability of winning is No Xenia s probability of winning is while Yolanda and Zoe each have a probability of No Xenia s probability of winning is while Yolanda and Zoe each have a probability of H T H T T H T H Zoes coin H H T T T T H H 10 Game 2 Xenia wins if there are 2 heads and 1 tails Yolanda wins if there are 2 tails and 1 heads Zoe wins if there are 3 heads or 3 tails Is this a fair game Answer choices Yes Each player a probability of winning is 2 Yes Each player s probability of winning is 8 No Zoe s probability of winning is while Xenia and Yolanda each have a probability of No Zoe s probability of winning is while

Airlines sometimes overbook flights Suppose that for a plane with 50 seats 55 passengers have tickets Define the random variable Y as the number of ticketed passengers who actually show up for the flight The probability mass function of Y appears in the accompanying table 47 46 0 10 0 11 48 0 14 49 0 25 51 52 0 06 0 05 Y 50 45 0 05 0 18 P Y a What is the probability that the flight will accommodate all ticketed passengers who show up 53 54 0 02 0 03 b What is the probability that not all ticketed passengers who show up can be accommodated What is this probability if you are the third person on the standby list 55 0 01 c If you are the first person on the standby list which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated what is the probability that you will be able to take the flight

7 A survey of magazine subscribers showed that 45 8 rented a car during the past 12 months for business reasons 54 rented a car during the past 12 months for personal reasons and 30 rented a car during the past 12 months for both business and personal reasons Identify the probability of renting a car for business or personal reasons 1 Point 0 698 0 998 0 30

The number of pumps in use at both a six pump station and a four pump station will be determined Give the possible values for each of the following random variables Enter your answers in set notation a T the total number of pumps in use T b x the difference between the numbers in use at stations 1 and 2 X c U the maximum number of pumps in use at either station U d Z the number of stations having exactly two pumps in use Z

The least squares regression line of this data set is y 0 295x 10 448 How many minutes does this line predict it will take a subject to minutes of television in the evening Round your answer to the nearest integer minutes Submit