# Probability Questions and Answers

Statistics

ProbabilityLet D be the event that a randomly chosen person has seen a dermatologist. Let S be the event that a randomly chosen person has had surgery for skin cancer. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen person has had surgery for skin cancer, given that the person has seen a dermatologist.
Select the correct answer below:
O P(DIS)
O P(D AND S)
O P(S) AND P(D)
O P(SID)

Statistics

ProbabilitySeventy cards are numbered 1 through 70, one number per card. One card is randomly selected from the deck. What is the probability that the number drawn is a multiple of 3 AND a multiple of 5?
• Enter your answer as a simplified fraction.
Provide your answer below:

Statistics

ProbabilityLet B be the event that a randomly chosen person has low blood pressure. Let E be the event that a randomly chosen person exercises regularly. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen person exercises regularly, given that the person has low blood pressure.
Select the correct answer below:
P(EB)
P(BE)
P(E) AND P(B)
P(B AND E)

Statistics

ProbabilityIf A and B are independent events with P(A) = 0.20 and P(A AND B)=0.12 find P(B).
Give your answer as a percentage, rounded to two decimal places if necessary.
Provide your answer below:

Statistics

ProbabilityA single card is randomly drawn from a standard 52-card deck. Find the probability that the card is a face card AND is red.
(Note: aces are not generally considered face cards, so there are 12 face cards. Also, a standard deck of cards is half red and half black.)
Provide the final answer as a fraction.

Statistics

ProbabilityA bag contains 35 marbles, 11 of which are red. A marble is randomly selected from the bag, and it is blue. This blue marble is NOT placed back in the bag. A second marble is randomly drawn from the bag. Find the probability that this second marble is NOT red.
• Provide the final answer as a fraction.

Statistics

ProbabilityStudents traveling to Spain on a study abroad trip have varying levels of Spanish proficiency. Of the students studying abroad, 7 students are fluent, 10 students are intermediate, and 2 students are beginners. If a single student is picked at random, what is the probability that the student is fluent or a beginner?
• Provide the final answer as a fraction.

Statistics

ProbabilityFor out second experiment. Set the Probability of Heads at 0.25, this will simulate a very biased coin. then fill in the table as you perform certain numbers of tosses. We will be comparing these probabilities as we go to look for patterns

Statistics

ProbabilityA card is drawn from a standard deck of 52 cards. Remember that a deck of cards has four suits: clubs, diamonds, hearts, and spades. Each suit has 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. Given the three events, which of the following statements is true? Select all that apply.
Event A: Drawing a clubs.
Event B: Drawing a spade.
Event C: Drawing a Queen.
Select all that apply:
Event B and Event Care mutually exclusive.
Event A and Event B are mutually exclusive.
Event A and Event Care not mutually exclusive.
Event A and Event Care mutually exclusive.

Statistics

ProbabilityYou are choosing a passcode for your new phone. It has to be a 6 digit code
using the numbers 0-9. You are allowed to repeat a number if you would like.
What is the probability that someone randomly guesses your combination on
the first try?
.
a.1 in 1,000,000
b. 1 in 151,200
c. 1 in 60,480
d. 1 in 531,441

Statistics

ProbabilityWhat is the conditional probability that you will randomly select a blue shirt if there are 15,000 shirts. Of those shirts 5,000 are blue
Select one:
a. 1/3
b. 5/15
c. 1/6
d. 1/5

Statistics

ProbabilityA certain medication has a side effect of a skin rash in 4% of the people who take the drug. Suppose 450 people take the drug and let X be the random variable that represents the number of people who experience a skin rash from the drug. Show and explain why a normal curve can be used to approximate the distribution.

Statistics

ProbabilityIn a high school graduating class of 100 students, 53 studied mathematics, 71 studied history, and 35 studied both mathematics and history. If one of these students is selected at random, find the probability that
(a) the student took mathematics or history,
(b) the student did not take either of these subjects;
(c) the student took history but not mathematics.
(a) if one of these students is selected at random, find the probability that the student took mathematics or history_____
Type an integer or a decimal. Do not round.)

Statistics

ProbabilitySuppose that in a senior college class of 500 students, it is found that 200 smoke, 241 drink alcoholic beverages, 207 eat between meals, 113 smoke and drink alcoholic beverages, 83 eat between meals and drink alcoholic beverages, 90 smoke and eat between meals, and 49 engage in all three of these bad health practices. If a member of this senior class is selected at random, find the probability that the student (a) smokes but does not drink alcoholic beverages; (b) eats between meals and drinks alcoholic beverages but does not smoke; (c) neither smokes nor eats between meals.
(a) P(smokes but does not drink alcoholic beverages)=
(Type an integer or a decimal. Do not round)

Statistics

ProbabilityA pair of fair dice is tossed. Find the probability of getting (a) a total of 11; (b) at most a total of 4.
(a) The probability of getting a total of 11 is__
(Simplify your answer.)

Statistics

Probability(a) If a letter is chosen at random from the English alphabet, find the probability that the letter is a consonant including y.
(b) If a letter is chosen at random from the English alphabet, find the probability that the letter is listed somewhere ahead of the letter t
(b) If a letter is chosen at random from the English alphabet, find the probability that the letter is listed somewhere after the letter k
(a) P(consonant including y) =
(Type an integer or a fraction.)
(b) P(ahead of the letter t) =
(Type an integer or a fraction.)
(c) P(after the letter k) =
(Type an integer or a fraction.)

Statistics

ProbabilityA professor has learned that four students in her class of 18 will cheat on the exam. She decides to focus her attention on seven
randomly chosen students during the exam.
a. What is the probability that she finds at least one of the students cheating? (Round your final answers to 4 decimal places.)
Probability
b. What is the probability that she finds at least one of the students cheating if she focuses on eight randomly chosen students?(Round your final answers to 4 decimal places.)
Probability

Statistics

ProbabilityAt 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

Statistics

ProbabilityTo get the ball back quickly in basketball, a coach decides to have one of his players foul a player on the opposing team, which gives the opposing team an opportunity to attempt a foul shot and score a point. Opposing player A makes 1/10 of the foul shots, B makes 3/10, C makes 5/10, and D makes 2/10. Which player should the team foul?
Opposing Player A
OOpposing Player B
OOpposing Player C
Opposing Player D

Statistics

ProbabilityThe probability that an industry will locate in City A is 0.5, the probability that it will locate in City B is 0.6, and the probability that it will locate in either City A or City B or both is 0.7. Complete parts (a) and (b) below.
(a) What is the probability that the industry will locate in both cities?
The probability is
(Type an integer or a decimal. Do not round.).
(b) What is the probability that the industry will locate in neither city?
The probability is
(Type an integer or a decimal. Do not round.)

Statistics

ProbabilityA survey of 25 randomly selected customers found the ages shown (in years). The mean is 33.12 years and the standard deviation is 10.20 years.
a) Construct a 90% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the confidence interval have been met.
b) How large is the margin of error?
c) How would the confidence interval change if you had assumed that the population standard deviation was known to be 11.0 years?
a) What is the confidence interval?
(Round to two decimal places as needed.)

Statistics

Probability(a) A poll taken in July 2010 estimates this proportion to be 0.32. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02?
A sample of __ adults is needed to obtain an 80% confidence interval with a margin of error of 0.02.

Statistics

ProbabilityAssume that T(n) = n for n≤2. For the questions below, find the tightest asymptotic upper bound and show the method you used to obtain it.
Show explanation, please.
1) T(n)=(T(n/2))²
2) T(n)=(T(√n))2
3) T(n)=T(2n/3)+log(n)

Statistics

ProbabilityA baseball player has a batting average of 0.28. What is the probability that he has exactly 4 hits in his next 7 at bats?

Statistics

ProbabilityIn a lottery game, a player picks six numbers from 1 to 30. If the player matches all six numbers, they win 50,000 dollars. Otherwise, they lose $1.
What is the expected value of this game? $___

Statistics

ProbabilityIn how many ways can 9 students be seated in a row of 9 chairs if Jack insists on sitting in the first chair?
Your answer is:___

Statistics

ProbabilityThe table shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012.
Year Seal Population Year Seal Population
(Thousands) (Thousands)
1997 3,493 2005 19,590
1998 5,282 2006 21,955
1999 6,357 2007 22,862
2000 9,201 2008 23,869
2001 11,224 2009 24,243
2002 12,964 2010 24,344
2003 16,226 2011 24,919
2004 18,137 2012 25,108
Let a represent time in years starting with a = 0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. Round any values to 4 decimal places.

Statistics

ProbabilityStudents at a certain college claim that the average distance students commute to campus is 26 miles per day. To check this claim, a random sample of 16 students is selected and their commuting distance is recorded. The average in the sample is 29 miles and the SD is calculated to be 8 miles. Is this evidence that the claim is incorrect?

Statistics

ProbabilityFrom past experience a stockbroker believes that under present economic conditions a customer will invest in tax-free bonds with a probability of 0.6, will
invest in mutual funds with a probability of 0.2, and will invest in both tax-free bonds and mutual funds with a probability of 0.13. Complete parts (a) and (b)
below.
(a) At this time, find the probability that a customer will invest in either tax-free bonds or mutual funds.
The probability that a customer will invest in either tax-free bonds or mutual funds is
(Type an integer or a decimal. Do not round.)

Statistics

Probability(a) It a letter is chosen at random from the English alphabet, find the probability that the letter is a consonant including y
(b) If a letter is chosen at random from the English alphabet, find the probability that the letter is listed somewhere ahead of the letter t
(b) If a letter is chosen at random from the English alphabet, find the probability that the letter is listed somewhere after the letter k
(a) P(consonant including y) =
(Type an integer or a fraction.)
(b) P(ahead of the letter t)=
(Type an integer or a fraction)

Statistics

ProbabilityExpress all answers as decimals rounded to 3 decimal places, if needed. Express percentages as decimals (instead of 25.6%, use .256
Cell phone users in Boise can choose between three carriers: Sprint, AT&T, and Verizon. Advertising by all three companies results in a continual shift of customers. Each year, Sprint loses 30% of customers to AT&T and 30% to Verizon. AT&T loses 20% to Sprint and 10% to Verizon. Verizon loses 25% to Sprint and 25% to AT&T. Currently, Sprint has 25% of the market, AT&T has 35%, and Verizon has 40%.
Use the order Sprint (S), AT&T (A), Verizon (V) throughout this assignment.
1. State the probability vector:
2. Create the transition matrix, labeling rows and columns, and draw the transition diagram.
Create your matrix with the rows ordered S, A, and V, and columns ordered S, A, and V.
3. Assume that for 5 years this trend continues. State the transition matrix after 5 years.
4. What is the market share for each company after 5 years?
Sprint:
AT&T:
Verizon:
5. If the trend continues indefinitely, what will the market share be for each in the long run?
Sprint:
AT&T:
Verizon:

Statistics

ProbabilityA firm has a required rate of return of 0.115. Its expected RE is 0.144 and expected earnings per
share are 1.8. If the firm's payout ratio is 0.51, what is the firm's sustainable or intrinsically
justifiable P/E ratio?
10.443
12.015
11.476
12.578
10.816

Statistics

ProbabilityGiven these DuPont ratios and equity per share:
Tax burden 0.79
Interest burden 0.64
Operating margin
Asset turnover 1.7
Leverage ratio 1.9
Avg Equity 28
Solve for current Net Income (EPSO) and --
What is the value of the firm using the DDM given the following:
Dividend ratio 0.36
Rate of return 0.2
Assume simple growth of ROE*b.
43.79
42.68
37.90
0.13
41.30
39.27

Statistics

ProbabilityTwenty-three subjects volunteer for a study of a new cold medicine. Ten of the volunteers are ages 20-39, 6 are ages 40-59, and 7 are age 60 or older. If 9 volunteers are selected at random, find the following probabilities.
(a) the probability that all the volunteers selected are ages 20-39
(b) the probability that 5 of the volunteers are ages 20-39 and 4 are age 60 or older
(c) the probability that 4 of the volunteers are ages 40-59

Statistics

ProbabilityThe populations of termites and spiders in a certain house are growing exponentially. The house contains 120 termites the day you move in. After four days, the house contains 210 termites. Three days after moving in, there are two times as many termites as spiders. Eight days after moving in, there were four times as many termites as spiders. How.long.(in.days) does it take the population of spiders to triple? (Round your answer to one decimal place.)
____days

Statistics

ProbabilityThe daily exchange rates for the five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.143 in currency A (to currency B) and
standard deviation 0.031 in currency A. Given this model, and using the 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely, complete parts a) through (d).
a) What is the probability that on a randomly selected day during this period, a unit of currency B was worth more than 1.143 units of currency A?
The probability is
(Type an integer or a decimal.)
b) What is the probability that on a randomly selected day during this period, a unit of currency B was worth less than 1.081 units of currency A?
The probability is .
(Type an integer or a decimal.)
c) What is the probability that on a randomly selected day during this period, a unit of currency B was worth less than 1.050 units of currency A?
The probability is%.
(Type an integer or a decimal.)

Statistics

ProbabilityOf all the River Club members in a particular city, 45% prefer swimming on weekends and 55% prefer swimming on weekdays. It is found that 10% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming and are female.
The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is? Show your work.

Statistics

ProbabilityIf a coin is flipped 8 times, what is the probability that it will show all heads or all tails? Show your work.

Statistics

ProbabilityHemoglobin Level
Less than 25 25-35 Above 35 Total
Years Years Years
Less than 9 21 32 76 129
Between 9 and 11 49 52 46 147
Above 11 69 44 40 154
Total 139 128 162 429
6. Based on the data in the two-way table, the probability of being older than 25 years and having a hemoglobin level above 11 is? Show your work.
7. The probability of having a hemoglobin level above 11 is? Show your work,
8. Being older than 36 years and having a hemoglobin level above 11 (are or are not, circle one) dependent on each other.

Statistics

ProbabilityFuture scientists: Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 28% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of 85 freshmen is selected. Round the answer to at least four decimal places.
Is it appropriate to use the normal approximation to find the probability that less than 30% of the freshmen in the sample are planning to major in a STEM
discipline?

Statistics

ProbabilityMany couples believe that it is getting too expensive to host an "average" wedding in the United States. According to a statistics study in the U.S., the average cost of a wedding in the U.S. in 2014 was $25,200. Recently, in a random sample of 35 weddings in the U.S. it was found that the average cost of a wedding was $24,224 with a standard deviation of $2,210. Construct and interpret a 95% confidence interval for the mean cost for the wedding in the U.S. (No work show = No point)

Statistics

Probability18. The FDA's Center for Food Safety and Applied Nutrition suggests the recommended dietary allowance (RDA) for calcium for woman aged 19 to 24 is 1200 milligrams per day. For women 25 and older, the allowance drops to 800 milligrams.
In a sample of 120 women aged 19 to 24, only 32 women met or exceeded the RDA for calcium. In another sample of 150 women aged 25 and older, 56 of them met or exceeded the RDA for calcium. Construct and interpret a 98% confidence interval for the difference in population proportions for the two age groups of women. (No work show = No point)

Statistics

ProbabilityA basket contains six apples, three oranges, ten corn, four pears and six peaches, You randomly select a fruit. What is the conditional probability of selecting a fruit that it is a orange? Select one:
a. 15.8%
b. 15%
c. 17.5%
d. 10.3%

Statistics

ProbabilityA multiple-choice test consists of 10 questions. Each question has answer choices of a, b, c, and d, 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.

Statistics

ProbabilityYou do a 2-sample hypothesis test where you check a person's weight before starting a diet, and then again after they finish the diet. What kind of samples do you take here?
a)Independent
b)Matched Pairs

Statistics

ProbabilityA dog allergy test for people has a 97.5% accuracy rate. Only 2% of the population has an allergy to dogs (actually it is much smaller than that!). Hint: Use a group of 100,000 people who've taken this test and the information provided to complete a table to answer the
following question:
If you tested negative, what is the probability you have a dog allergy? (Round your probability to the nearest thousandth of a
percent!)
Probability = ___________ %

Statistics

ProbabilityA major ride-sharing company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $25.03 with a standard deviation of $3.41. Based on this information, complete the following statements about the distribution of the company's fares from O'Hare Airport to the Drake Hotel.
(a) According to Chebyshev's theorem, at least (Choose one) of the fares lie between 18.21 dollars and 31.85 dollars.
(b) According to Chebyshev's theorem, at least (Choose one) of the fares lie between 19.92 dollars and 30.15 dollars.

Statistics

ProbabilityFill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are 0, 3, 4, 5, and 6.
Value x of X P(X = x)
0 0.15
3 0.27
4 _____
5 _____
6 0.17

Statistics

ProbabilityThe workers' union at a particular university is quite strong. About 94% of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview 5 workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly 2 of the workers interviewed are union members? Round your response to at least three decimal places.