Probability Questions and Answers

(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)

Express 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:

A 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

Given 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

Twenty-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

The 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

The 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.)

Of 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.

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

Conditional Probability with Bayes's Theorem: P(A|B) = P(B|A) x P(A) / P(B)

Hemoglobin 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.

Future 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?

Many 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)

18. 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)

A 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%

A 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.

You 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

A 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 = ___________ %

A 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.

Fill 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

The 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.

A 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.)

A 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.)

An 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) _____ _____ ______ _____

The 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

Ace 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.

A 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.

The 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.

An 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) ______ _______ ______

Fill 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

Roughly 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%

Your 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.

Let 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

Your 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.

Consider 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.

Anita'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.)

Suppose 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.

Directions: 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.

A 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) = _________, __________, _____________.

Thirty-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.

A 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.

A 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

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

When 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.

At 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.

A 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.

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(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)

The 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 : _____

Use 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.

Consider 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.