Probability Questions and Answers

Casey is looking to rent a two-bedroom apartment in one of two towns, Gardiner or Augusta. He randomly selects 100 two- bedroom apartments from both towns and records the area of each apartment. Both towns have a two-bedroom apartment that has an area of 645 square feet. Based on the z-scores you calculated above, which of the two towns is more likely to have a two-bedroom apartment with 645 square feet? Select the correct answer below: The absolute value of the z-score for the apartment in Gardiner is greater than for the apartment in Augusta, so the apartment in Gardiner having an area of 645 square feet is more likely. The absolute value of the z-score for the apartment in Gardiner is less than for the apartment in Augusta, so the apartment in Gardiner having an area of 645 square feet is more likely. The absolute value of the z-score for the apartment in Augusta is greater than for the apartment in Gardiner, so the apartment in Augusta having an area of 645 square feet is more likely. The absolute value of the z-score for the apartment in Augusta is less than for the apartment in Gardiner, so the apartment in Augusta having an area of 645 square feet is more likely.

Consider the following binomial distribution scenario. A softball pitcher has a 0.675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If the softball pitcher throws 29 pitches, we want to know the probability that exactly 19 of them are strikes. Consider strikes as successes in the binomial distribution. Identify the numerical value of the parameter p.

The amount of time it takes Annie to make dinner is continuous and uniformly distributed between 19 minutes and 49 minutes. What is the probability that it takes Annie between 39 and 40 minutes given that it takes less than 44 minutes for her to make dinner?

What is all individuals, objects, or measurements whose properties are being studied? Select the correct answer below: population variable statistic data

If X ≈ U(4.5,18.5) is a continuous uniform random variable, what is P(X > 6)? Select the correct answer below: 1/7 1/2 11/14 25/28 13/14

The amount of time it takes William to wait for the bus is continuous and uniformly distributed between 4.5 minutes and 14.5 minutes. What is the probability that it takes William more than 7 minutes to wait for the bus? Select the correct answer below: 1/5 2/5 3/4 4/5 17/20

The event a teen wins a video game is A and the eventa mom buys groceries is B. If these events are independent events, using P(A) = 0.78, and P(B) = 0.82, what is P(A/B)? Provide your answer below:

Suppose that we have a sample space S = E₁, E2, E3, E4, E5 where E denotes the sample points. Following probability assignments apply: P(E₁) = 0.05, P(E₂) = 0.15, P(E3) = 0.3, P(E4) = 0.25, P(E5)= 0.3. a. Does the above assignment of probability make sense to you? And if not then why? b. Ignoring the errors (if any) what is P(AUB) if A = {E₁, E3} and B = {E₁, E4}?

(a) A perfectly balanced coin is tossed 3 times and tail appears on all 3 tosses. Calculate probability of a tail on the 4th trial. (b) An economist predicts a 60% chance of recession in country A and a 25% chance of recession in country B. There is 64% chance of a recession in country A given that country B is in recession. What is the probability that country B in recession given that country A in recession?

Give the numerical value of the parameter n in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.597 and without a popcorn coupon is 0.403. If you buy 18 movie tickets, we want to know the probability that no more than 13 of the tickets have popcorn coupons. Consider tickets with popcorn coupons as successes in the binomial distribution. Do not include n - in your answer.

Suppose A and B are mutually exclusive events, and that P(A) = 0.13 and P(B) = 0.85. Find P(A OR B).

Give the numerical value of the parameter p in the following binomial distribution scenario. A softball pitcher has a 0.721 probability of throwing a strike for each pitch and a 0.279 probability of throwing a ball. If the softball pitcher throws 19 pitches, we want to know the probability that more than 15 of them are strikes. Consider strikes as successes in the binomial distribution. Do not include p = in your answer.

A deck of cards contains RED cards numbered 1, 2, 3, BLUE cards numbered 1, 2, 3, 4, 5, and GREEN cards numbered 1, 2, 3, 4. If a single card is picked at random, what is the probability that the card is RED? Select the correct answer below: 8/12 2/12 9/12 3/12 10/12 4/12

Given the following information about events A B, and C: P(A) = 0.62 P(B) = 0.34 P(C) = 0.07 P(B|A) = 0 P(C|B) = 0.34 P(AIC) = 0.62 Are events A and B mutually exclusive, independent, or both? Select the correct answer below: A and B are mutually exclusive because P(B|A) = 0. A and B are not mutually exclusive because P(BA) ≠ P(B). A and B are independent because P(B|A) = P(B). A and B are neither mutually exclusive nor independent.

If the probability of a student taking a calculus class is 0.10, the probability of taking a statistics class is 0.90, and the probability of taking a calculus class and a statistics class is 0.07, what is the probability of a student taking a calculus class or a statistics class?

A college has buildings numbered from 1 through 60. What is the probability that a student will have their first class in a building number that is not a multiple of 8? • Give your answer as a fraction. Reduce the fraction if necessary.

Suppose that X is a discrete random variable which takes on values: 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, and suppose further that Y is a continuous random variable that is a good approximation for X. Which one of the following approximates Pr[39< X <44]? A. Pr[41.5 < Y < 46.5] B. Pr(41.5 < Y < 41.5] C Pr[36.5< Y <41.5] D.Pr[36.5 < Y < 46.5] E. Pr[39< Y < 44]

With a rectangular metal sheet 24 cm wide and 120 cm long, you want to build a channel, for which you will bend along the sheet, a length x y an angle θ. Use Lagrange multipliers to determine the value of x and θ so that the channel drive maximum volume.

Assume that the population standard deviation is o=0.6. If appropriate, perform a hypothesis test at the a=0.01 level to determine whether the mean GPA for business students differs from the mean GPA at the whole university. What do you conclude? Use the P-value method with the TI-84 calculator. State the null and alternate hypotheses. Ho: H₁: This hypothesis test is a two-tailed Compute the P-value of the test statistic. Round the answer to at least four decimal places. P-value=

The event of pedestrians walking is A and the event of cars pulled over for speeding is B. If these events are independent events, and P(A) = 0.27, and P(B) = 0.71, what is P(B/A)? Provide your answer below:___

Let 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)

Seventy 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:

Let 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)

If 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:

A 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.

A 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.

Students 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.

For 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

A 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.

You 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

What 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

A 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.

In 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.)

Suppose 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)

A 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.)

(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.)

A 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

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

To 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

The 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.)

A 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.)

(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.

Assume 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)

A 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?

In 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? $___

In 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:___

The 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.

Students 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?

From 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.)

(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)