# Probability Questions and Answers

Statistics

ProbabilityA multiple-choice test consists of 8 questions. Each question has answer choices of a, b, c, d, and e, and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that he gets at least 2 of them correct? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

Statistics

ProbabilityA rainstorm in Portland, Oregon, has wiped out the electricity in about 10% of the households in the city. A management team in Portland has a big meeting tomorrow, and all 6 members of the team are hard at work in their separate households, preparing their presentations. What is the probability that none of them has lost electricity in his/her household? Assume that their locations are spread out so that loss of electricity is independent among their households.
Round your response to at least three decimal places. (If necessary, consult a list of formulas.)

Statistics

ProbabilityAn number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string of the sort oee (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll).
For each outcome, let N be the random variable counting the number of odd rolls in each outcome. For example, if the outcome is ooe, then N (ooe) = 2.
Suppose that the random variable X is defined in terms of N as follows: X=2N-3. The values of X are given in the table below.
Outcome ooe eoo ooo oee oeo eeo eoe eee
Value of X 1 1 3 -1 1 -1 -1 -3
Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.
Value x of X _____ _____ ______ _____
P(X=x) _____ _____ ______ _____

Statistics

ProbabilityThe WHO published a study indicating that the global healthy life expectancy has increased by 9.3% from 2000 to 2019. In 2000, the global healthy life expectancy was 58.3 years. Use this information to determine the global healthy life expectancy for 2019. How many more years of life were added to the global healthy life expectancy from 2000 to 2019?
a. 5.9 years
b. 4.7 years
c. 4.9 years
d. 6.0 years
e. 5.4 years

Statistics

ProbabilityAce Pet Store
(Varieties of Rats In Stock)
Short-hair Long-hair Total
Male 65 30 95
Female 55 40 95
Total 120 70 190
What is the probability that a rat chosen at random is long haired and Female?
Express your answer as a percentage, rounded to the nearest hundredth of a percent if necessary.

Statistics

ProbabilityA dog allergy test for people has a 98% accuracy rate. Only 1% of the population has an allergy to dogs (actually it is much smaller than that!). Use a group of 100,000 people who've taken this test and the information provided to complete a table and answer the following question: If you tested negative, what is the probability you have a dog allergy?
Round your answer to the nearest hundredth of a percent.

Statistics

ProbabilityThe average woman's height is 65 inches with a standard deviation of 3.5 inches.
a.) Determine the Z-score of a woman who is 70 inches tall.
b.) Use a z-score table to determine how many women out of 10,000 would be taller than the 70 inch tall woman.

Statistics

ProbabilityAn ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc.
For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is hth, then N (hth) = 1. Suppose that the random variable X is defined in terms of N as follows: X= 2N-2N^2-2. The values of X are given in the table below.
Outcome ttt hht thh tht tth hhh htt hth
Value of X -14 - 2 - 2 -6 -6 -2 -6 -2
Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.
.
Value x of X ______ _______ ______
P(X=x) ______ _______ ______

Statistics

ProbabilityFill in the P(X= x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are 2, 3, 4, 5, and 6.
Value x of X P(x = x)
2 0.28
3 0.12
4 0.11
5 0.22
6 0.28

Statistics

ProbabilityRoughly 1% of the population will have an allergic reaction to a certain type of bee sting. The table below shows the predicted testing outcome for a test that is 95% accurate.
Positive Test Negative Test Total
Has allergy to 95 5 100
bee sting
Does not have
allergy to bee 495 9405 9900
sting
Total 590 9410 10,000
Given you received a negative test result, which of the following represents the probability that you do not have an allergy to this bee sting?
A) 0.1%
B) 5%
C) 95%
D) 16.1%
E) 99.9%

Statistics

ProbabilityYour friend weighs 83 kg. How many pounds is this?
Round your answer to the nearest tenth of a pound. Do not include units with your answer.

Statistics

ProbabilityLet X be a random variable with the following probability distribution.
Value x of X P(X=x) no
10 0.25
20 0.05
30 0.25
40 0.30
50 0.15
Complete the following. (If necessary, consult a list of formulas.)
(a) Find the expectation E (X) of X.
E(X) = 30.5
(b) Find the variance Var(x) of X.
Var(X) = 195

Statistics

ProbabilityYour friend Jeanie Alahgee has researched her family tree and finds that a large number of her family members have either red hair or blond
air and either green eyes or blue eyes. She makes a list of these family members and records her data below:
Blue Eyes Green Eyes Total
Blond 63 25 88
Red head 16 21 37
Total 79 46 125
What is the probability that a person chosen at random from Jeanie's list will have red hair and blue eyes?
Round your answer to the nearest tenth of a percent. Do not include units with your answer.

Statistics

ProbabilityConsider the following table:
Female Male Total
Republican 105 115 220
Democrat 150 103 253
Independent 150 179 329
Total 405 397 802
What is the probability a voter is either male or Republican?
Express your answer as a percentage correctly rounded to the nearest whole percent.

Statistics

ProbabilityAnita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that 45% of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of 5 customers at Anita's, exactly 4 order their food to go?
Round your response to at least three decimal places. (If necessary, consult a list of formulas.)

Statistics

ProbabilitySuppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true. P(c ≤ Z ≤0.83) = 0.7693 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

Statistics

ProbabilityDirections: Answer each question to the best of your ability. Show your work. No points will be given for answers only. You can use your calculator and pen/pencil.
1. The following table lists the probability distribution of the number of blood pressure monitors sold per day in a local pharmacy.
a) Find the value of the missing probability?
b) Find the probability P(x > 1) to the nearest tenth.
c) Calculate the mean, variance and standard deviation of this probability distribution.

Statistics

ProbabilityA number from 1-72 is chosen at random. Find each probability as a fraction (in simplest form). decimal, and percent.
Round the decimal to the nearest thousandth.
P(factor of 72 and even) = _________, __________, _____________.

Statistics

ProbabilityThirty-nine percent of U.S. adults think that the government should help fight childhood obesity. You randomly select six U.S. adults. Find the probability that the number of U.S. adults who think that the government should help fight childhood obesity is
(a) exactly three
(b) at least three.
(c) less than five.

Statistics

ProbabilityA multiple-choice examination consists of 75 questions, each having possible choices a, b, c, d, and e. Approximate the probability that a student will get at
most 16 answers correct if she randomly guesses at each answer. (Note that, if she randomly guesses at each answer, then the probability that she gets any one
answer correct is 0.2.) Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.

Statistics

ProbabilityA jar has 2 red marbles 2 blue marbles. Two marbles are chosen from the jar without replacement.
a) The probability that the marbles are the same color is
b) The probability that at least one of the marbles is red is
c) The probability that the marbles are NOT the same color is

Statistics

ProbabilityGiven a standard normal distribution, what is the value of
P(Z < 1.32 or z > 2.51)=
0.9066
0.9126
0.0874

Statistics

ProbabilityWhen a card is drawn from a deck, find the probability of getting the following.
(a) a King or black
(b) a card less than 6 or is a Heart.

Statistics

ProbabilityAt a used car lot, 8 different car models are to be parked close to the street for easy viewing, but there is only space for 6 cars. The employees want to determine how many ways can 6 of the 8 cars be arranged in the used car lot
Employee John says this is a permutation while employee Chris says this is a combination. Explain who is correct and algebraically determine the how many ways that the cars can be arranged.

Statistics

ProbabilityA researcher believes that about 72% of the seeds planted with the aid of a new chemical fertilizer will germinate. He chooses a random sample of 110 seeds
and plants them with the aid of the fertilizer. Assuming his belief to be true, approximate the probability that fewer than 77 of the 110 seeds will germinate. Use the normal approximation to the binomial with a correction for continuity.
Round your answer to at least three decimal places. Do not round any intermediate steps.

Statistics

ProbabilityA box contains 5 red marble(s), 2 blue marble(s), and 1 white marble(s). The marbles are selected at random, one at a time, and not replaced. Find P(white, then blue) as a fraction/ decimal _____ which is _____% (round answer to nearest hundredth)
A box contains 5 red marble(s), 2 blue marble(s), and 1 white marble(s). The marbles are selected at random, one at a time, and not replaced. Find P(red, then red) as a fraction/decimal __________
which is ____ % (round answer to nearest hundredth)
A box contains 5 red marble(s), 2 blue marble(s), and 1 white marble(s). The marbles are selected at random, one at a time, and not replaced. Find P(red, then white, then blue) as a fraction/decimal ____ which is ____ % (round answer to nearest hundredth)

Statistics

ProbabilityThe breaking strengths of cables produced by a certain manufacturer have a standard deviation of 83 pounds. A random sample of 80 newly manufactured cables has a mean breaking strength of 1750 pounds. Based on this sample, find a 90% confidence interval for the true mean breaking strength of all cables produced by this manufacturer. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Lower limit:______
Upper limit : _____

Statistics

ProbabilityUse the table provided: An Ivy Tech Campus completed a study tracking the semester that students will finish their degree and whether they intend to participate in the graduation ceremony. The table below shows the result Will Attend Graduation Will Not Attend Graduatiol Total
Summer 24 86 110
Fall 102 408 510
Spring 254 126 380
Total 380 620 1000
What is the probability that a student chosen at random from the study completed their degree in Fall and Will Attend Graduation? Write your answer as a decimal to the thousandths place.

Statistics

ProbabilityConsider the chart below of living arrangements.
Apartment Condo House Total
Single 206 62 34 302
Married 61 50 122 233
Total 267 112 156 535
What is the probability that a randomly selected person will have an apartment?
Write your answer as a decimal to the thousandths place.

Statistics

ProbabilitySuppose that 42% of the population of U.S. voters favors a particular presidential candidate. If a random sample of 75 voters is chosen, approximate the probability that at least 32 favor this candidate. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.

Statistics

ProbabilityEach number from 1 to 15 is written on a ball, then put in a bag. The balls are selected randomly and then replaced.
Find P(even, then odd) as a decimal/fraction _________ which is _________ % (round answer to the nearest hundredth)
Each number from 1 to 15 is written on a ball, then put in a bag. The balls are selected randomly and then replaced.
Find p(even, then number larger than 12) __________ as a decimal/fraction which is _________ % (round answer to the nearest hundredth)

Statistics

ProbabilityA standardized test has four forms - A, B, C, and D. Each form comes in three colors - red, blue, purple, yellow, and green.
a) How many different tests are created, based on form and color?
b) What is the probability that Linh receives a blue Form A test?
c) What is the probability that Manuel receives a yellow or green test?

Statistics

ProbabilityWhile studying to be a vet, Brad learns that different animals have different heart rates. This table shows the resting heart rate of a small dog:
Small dog
Time (minutes) Heartbeats
3 300
4 400
5 500
This equation describes the resting heart rate of a typical cat, where y represents the number of heartbeats and x represents the number of minutes:
y = 150x
Which animal has a slower heart rate?
a cat
a small dog
How much slower is its heart rate?
_________beats per minute slower

Statistics

ProbabilityUse the ALEKS calculator to solve the following problems.
(a) Consider a t distribution with 10 degrees of freedom. Compute P(-1.55 <t<1.55). Round your answer to at least
three decimal places.
P(-1.55 <t< 1.55) =
(b) Consider a t distribution with 16 degrees of freedom. Find the value of c such that P(t> c)=.
Round your answer to at least three decimal places.
c=

Statistics

ProbabilityIn a school, 30% 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. Hint: First, count all of the random numbers that contain a 2, 4, or 8.
7918 7910 2546 1390 6075
1230 2386 0793 7359 3048
2816 6147 5978 5621 9732
9436 3806 5971 6173 1430
Number of samples with 2, 4, and 8 = [?]

Statistics

ProbabilityThe following data gives annual salaries (in thousands) of randomly chosen employees with college degrees. Some of these employees have only Bachelors' degrees and some have Masters'/PhDs. At α =0.05, can we claim that the mean salaries of employees with Bachelors' degrees are lower?
Bachelors': 89 78 67 89 100 65 45 37 68 68 78 80
Masters'/PhDs: 120 130 78 69 88 101 112 160 200 88
Test using: (a) a hypothesis test (b) a confidence interval

Statistics

ProbabilityEach person has a 75% probability of going to the Tahoe restaurant. You randomly select 8 people.
(a) What is the probability that 4 people will go to the restaurant?
(b) What is the probability that more than 6 people will go to the restaurant ?
(c) What is the probability that at most 7 people will go to the restaurant ?

Statistics

Probability100 adults and 100 teenagers were polled and asked if they liked the food choices found in the local food court at the mall. 21 of the adults liked the food court choices, and 96 of the teenagers liked the food court choices.
a) Make a two-way table for this data that shows the joint and marginal frequencies.
b) Make a two-way table that shows the joint and marginal relative frequencies.
c) Make a two-way table that shows the conditional relative frequencies based on the column totals.
d) What conclusions can you draw based on your results? Explain.

Statistics

ProbabilityThe monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $12. Find the probability that a randomly selected utility bill is greater than $90.

Statistics

ProbabilityYou are measuring the length of squirrels from different sides of the Grand Canyon, to see if they are different species. Which of the following techniques should you use?
(a)Two sample t-test
(b)Fisher Exact Test
(c)adjusted Wald interval
(d)geometric mean

Statistics

ProbabilityIf four out of four test subjects successfully complete a task, which of the following is the correct way to report your results?
With 95% confidence, [0.454, 1.056 ]percent of people will successfully complete this task.
With 95% confidence, over 45% of people will successfully complete this task.
With 95% confidence, [0.40, 0.76] of people will successfully complete this task.
With 95% confidence, only 45% of people will not successfully complete this task.

Statistics

ProbabilityJeremy will roll a number cube numbered 1-6 twice. What is the probability of rolling an even number, then the number 3?

Statistics

ProbabilityThe cafeteria staff made sandwiches. Each sandwich had either rye or wheat bread, either ham or turkey, and either cheese or no cheese. The staff made an equal number of each type of sandwich. The sandwiches were placed on a tray. Without looking, Mary will choose a sandwich. What are the chances that Mary will get a sandwich with cheese?

Statistics

ProbabilityThe vanilly mandelic acid test is a urine test which was developed to detect the presence of neuroblastoma, a rare serious disease. This test gives a positive result in 70% of cases of neuroblastoma. 8 children with neuroblastoma are administered this test. We want to calculate the probability that the test will give an incorrect (negative) result for at least 2 children in this group. Which one of the following R commands gives this probability?
A) pbinom(2,8,0.7)
B) 1-pbinom (1,8,0.7)
C) pbinom(1,8,0.7)
D) pbinom (2,8,0.3)
E) 1-pbinom (1,8,0.3)

Statistics

Probabilityin the California Community Colleges an undergraduate student survey was taken that compares the class of the student to their opinion on whether or not they favor or oppose same sex marriages. The following data is a summary of the survey taken by questioning 500 under -graduate students. If a student from the survey is selected at random, then find the probability that the student favors same-sex marriages, given that the student is not a Senior
Fresh Soph Junior Senior Totals
Favor 85 74 64 53. 276
Oppose 61 60 55 48. 224
Totals 146 134 119 101 500
a)223/500
b)276/399
c)223/399
d)399/500

Statistics

ProbabilityIn a busy coffee shop, which is a member of an international chain of coffee shops, 40% of customers order a pastry in addition to their drink. If 20 customers were selected at random during one business day, what is the probability that at least 11 of them did not order a pastry with their drink. Round your answer to 4 decimal places.
a)0.1275
b)0.3763
c)0.5956
d)0.7553
e)None of the above

Statistics

ProbabilityA spinner is divided into blue, yellow, and red parts. Gianna spun this spinner 400 times and listed her results in the table below. Select all of the estimated probabilities of the spinner landing on red.
COLOR FREQUENCY
Blue 198
Yellow 106
Red 96
A. 1/5
B. 6/25
C. 0.95
D. 0.24
E. 24%

Statistics

ProbabilityCompute the amount of interest earned in the following simple interest problem. A deposit of $4,500 at 5% for 3 years:
$67.50
$6.75
$675.00
$6,750.00