Based on the table, which of the following statements is correct?

The probability of selecting a dog that tested positive is greater than 0.5. The probability of selecting a dog that lived mostly indoors is greater than 0.5. The probability of selecting a dog that tested positive is greater than the probability of selecting a dog that tested negative. The probability of selecting a dog that tested positive given that the dog lived mostly outdoors is less than the probability of selecting a dog that tested positive given that the dog lived mostly indoors. The probability of selecting a dog that lived mostly outdoors given that the dog tested positive is greater than the probability of selecting a dog that lived mostly outdoors given that the dog tested negative.

A high school science teacher has 78 students. Of those students, 35 are in the band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One student from the 78 students will be selected at random. Let event B represent the event of selecting a student in the band, and let event S represent the event of selecting a student on a sports team. Are B and S mutually exclusive events?

A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20. Which of the following is the best interpretation of the probability 0.20?

The table shows data that were collected from people who attended a certain high school basketball game and indicates the team each person rooted for and whether each of these people purchased food during the game. A person who attended the game will be selected at random. Which of the following correctly interprets mutually exclusive events represented by the table?

A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately ¼ of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item?

In a certain population of birds, about 40 percent of the birds have a wingspan greater than 10 inches. Biologists studying the birds will create a simulation with random numbers to estimate the probability of finding 1 bird in a sample of 6 birds with a wingspan greater than 10 inches. Which of the following assignments of the digits 0 to 9 will model the population?

Let the random variable B represent the number of books a student buys at the next book fair. What is the expected value of B?

Each person in a group of twenty people at a hotel orders one meal chosen from oatmeal, eggs, or pancakes and one hot beverage chosen from coffee or tea. One person will be selected at random from the twenty people. What is the sample space for the meal and beverage for the person selected?

At a local elementary school, 35 percent of all students have brown eyes, 45 percent have brown hair, and 60 percent have brown hair or brown eyes. A student will be selected at random from the school. Let E represent the event that the selected person has brown eyes, and let H represent the event that the selected person has brown hair. Are E and H mutually exclusive events?

At a sporting event, cheerleaders will throw 50 bundled T-shirts into the crowd. The T-shirt sizes consist of 10 small, 15 medium, and the remainder either large or extra large. Suppose Ana catches a T-shirt. What is the probability that she will catch a T-shirt that is not a size small?

Let the random variable X represent the amount of money won or lost for a player who pays $1 to play a certain carnival game. The following table shows the probability distribution of X.

The expected value of W is:

The mean, or expected value, for a discrete random variable, X, is μX = Σ xiP(xi). If the random variable X represents the value of the prize won for a single ticket minus the cost of the ticket, then:

A middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two students from the club will be selected at random to participate in the county chess tournament. What is the probability that Adam and Ella will be selected?

A prize game at a circus has a spinner with 12 sections, where each section is equally likely to be selected when the spinner is spun. There are 7 blue sections and 5 orange sections. Camille has spun the spinner 4 times and the pattern of outcomes was orange, blue, orange, blue. Camille will spin the spinner two more times. Which of the following statements is true?

At Mike’s favorite coffee shop, the coffee of the day is either a dark roast, a medium roast, or a light roast. From past experience, Mike knows that the probability of the coffee being a light roast is 0.15 and the probability of the coffee being a dark roast is 0.25. What is the probability of the coffee of the day not being a light roast or a dark roast on the next day that Mike visits the coffee shop?

Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?

A city department of transportation studied traffic congestion on a certain highway. To encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2. The probability distribution of the number of people in passenger cars on the highway is shown in the table.

The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer. Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the mean cost per customer for the performance?

Let random variable S represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable S. Alfonso claims that the distribution of S is symmetric with a mean age of 36. Does the histogram support Alfonso’s claim?

Study Material First Half of Probability

One student from a high school will be selected at random. Let A be the event that the selected student is a student athlete, and let B be the event that the selected student drives to school. If P(A ∩ B) = 0.08 and P(B|A) = 0.25, what is the probability that the selected student will be a student athlete?

Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6?

The probability distribution of the number of cookies sold by a store each day is shown in the table below. The store earns a profit of $0.50 per cookie sold. What is the store’s expected daily profit for the sales of the cookies?

What is the frequency of bur oak trees with a diameter of 10 inches?

What is the cumulative frequency for trees with a diameter of 16 inches?

What is the cumulative relative frequency for trees with a diameter of 38 inches?

Which tree diameter has the highest frequency?

What is the relative frequency of trees with a diameter of 25 inches?

How many trees have a diameter greater than or equal to 30 inches?

Which of the following differences in cumulative relative frequencies gives the proportion of trees that are 12 inches to 16 inches, inclusive, in diameter?

As a promotion, the first 50 customers who entered a certain store at a mall were asked to choose from one of two discounts. The first discount choice was 20% off all purchases made that day. The second discount choice was 10% off all purchases for the week. Of those who received the discounts, 28 chose the first discount and 22 chose the second discount. One customer will be selected at random from those who received a discount. Let F represent the event that the selected person chose the first discount, and let S represent the event that the selected person chose the second discount. Are F and S mutually exclusive events?

Based on the simulation, what is the probability that at most 2 of the next 10 callers will have to wait more than 8 minutes to have their calls answered?

For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?

What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X?

At a certain bakery, the price of each doughnut is $1.50. Let the random variable D represent the number of doughnuts a typical customer purchases each day. The expected value and variance of the probability distribution of D are 2.6 doughnuts and 3.6 (doughnuts)^2, respectively. Let the random variable P represent the price of the doughnuts that a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of the probability distribution of P?

What is the price of each doughnut, $1.50, multiplied by the standard deviation of the number of doughnuts $$\sqrt{3.6}$$ ?

The probability that a particular electrical component operates successfully is $$\frac{3}{4}$$ . An electrical system consists of three such components that operate independently. The system will function successfully if at least one of the three components operates successfully. What is the probability that the system will function successfully?

32. The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation?

The number of breakdowns on a randomly selected day is expected to be 0.28.

Ali surveyed 200 students at a school and recorded the eye color and the gender of each student. Of the 80 male students who were surveyed, 60 had brown eyes. If eye color and gender are independent, how many female students surveyed would be expected to have brown eyes?

A magazine has 1,620,000 subscribers, of whom 640,000 are women and 980,000 are men. Thirty percent of the women read the advertisements in the magazine and 50 percent of the men read the advertisements in the magazine. A random sample of 100 subscribers is selected. What is the expected number of subscribers in the sample who read the advertisements?

A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company's claim is correct, what is the expected number of nondefective lightbulbs in a random sample of 1,000 bulbs?

What is the value represented by the options?

What profit does XYZ Office Supplies Company expect to make for the next year if the profit from each calculator sold is $$20 at wholesale and$$ 30 at retail?

A mathematics competition uses the following scoring procedure to discourage students from guessing on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?

In a certain game, a fair die is rolled and a player gains 20 points if the die shows a "6." If the die does not show a "6," the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?

A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags?

The random variable X takes on the values of 2, 5, n, and 15. The probability distribution of X is shown in the following table. X: 2 5 n 15 P(X): 0.1 0.4 0.2 0.3 The expected value of X is 9.1. What is the value of n?

A fair coin will be tossed three times. The set of possible outcomes may be described by the ordered triples {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, where H represents heads and T represents tails. What is the probability that all three tosses result in heads, given that the three tosses result in more heads than tails?

A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3?

Let random variable U represent the field goal percentage (percentage of shots made) for players in a basketball league. The following table shows the probability distribution of the random variable U. Fatima claims that the distribution of U is uniform with a median of 0.4 field goal percentage. Is Fatima’s claim supported by the table?

Mateo plays on his school basketball team. From past history, he knows that his probability of making a basket on a free throw is 0.8. Suppose he wants to create a simulation using random numbers to estimate the probability of making at least 3 baskets on his next 5 free throw attempts. Which of the following assignments of the digits 0 to 9 could be used for the simulation?

From those who purchased the lunch special that day, one student will be selected at random. What is the probability that the student selected will be in grade 10 given that the student ordered french fries as the side order?

Amy has 12 brown golf tees, 8 white golf tees, 10 red golf tees, 6 blue golf tees, and 12 green golf tees in her golf bag. If she selects one of the tees from the bag at random, what is the probability that she selects a tee that is not brown or blue?

There are 48 total tees in the bag, and 30 of the tees are a color other than brown or blue. What is the probability that a tee selected at random will be a color other than brown or blue?

The seniors at three high schools were surveyed about their plans after graduation. One senior from the high schools will be selected at random. What is the probability that the senior selected will not be from High School B given that the senior responded with a choice other than college?

The number of points obtained in one game is independent of the number of points obtained in a second game. When the game is played twice, the sum of the number of points for both times could be 0, 1, 2, 3, or 4. If Y represents the sampling distribution of the sum of the scores when the game is played twice, for which value of Y will the probability be greatest?

Data were collected on the number of days per week that members visit a certain fitness center. The values varied from 0 to 7, and a distribution of relative frequencies for the values was created. Let the random variable X represent the number of days per week that a member visits. The mean of X is 3.12. Which of the following statements is the best interpretation of the mean?

A hockey all-star game has the Eastern Division all-stars play against the Western Division all-stars. On the Eastern Division team there are 8 United States-born players, 14 Canadian-born players, and 2 European-born players. On the Western Division team there are 12 United States-born players, 8 Canadian-born players, and 4 European-born players. If one player is selected at random from the Eastern Division team and one player is selected at random from the Western Division team, what is the probability that neither player will be a Canadian-born player?

The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that the probability of being awarded the first job (event A) is 0.75; the probability of being awarded the second job (event B) is 0.5; and the probability of being awarded both jobs (event (A and B)) is 0.375. If the owner’s beliefs are correct, which of the following statements must be true concerning event A and event B?

Event A and event B are mutually exclusive and are independent.

Given independent events A and B such that P(A) = 0.3 and P(B) = 0.5, which of the following is a correct statement?

For which of the following probability assignments are events A and B independent?

A nonprofit organization plans to hold a raffle to raise funds for its operations. A total of 1,000 raffle tickets will be sold for $$1.00 each. After all the tickets are sold, one ticket will be selected at random and its owner will receive$$ 50.00. The expected value for the net gain for each ticket is -$0.95. What is the meaning of the expected value in this context?

The random variable W can take on the values of 0, 1, 2, 3, or 4. The expected value of W is 2.8. Which of the following is the best interpretation of the expected value of random variable W?