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?

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?

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?

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?

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?

An online customer service department estimates that about 15 percent of callers have to wait more than 8 minutes to have their calls answered by a person. The department conducted a simulation of 1,000 trials to estimate the probabilities that a certain number of callers out of the next 10 callers will have to wait more than 8 minutes to have their calls answered. The simulation is shown in the following histogram.

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?

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?

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?

The seniors at three high schools were surveyed about their plans after graduation. The following table shows the responses, classified by high school.

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?

A store owner reports that the probability that a customer who purchases a lawn mower will also purchase an extended warranty is 0.68.

Which of the following is the best interpretation of the probability 0.68?

The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey.

Is Avery interpreting the probability correctly?

Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. The students were classified by their age. The following table summarizes the responses of the students by age-group.

One student from the school will be selected at random. What is the probability that the student is in the age-group of 6 to 8 years given that the selected student responded joy?

In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. One car will be selected at random from the parking lot. If each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green?

Joslyn performed an experiment using a die with its faces numbered from 1 to 6. She rolled the die and recorded whether the 5 landed face up. She repeated the process many times and kept a cumulative record of the total number of rolls and the total number of 5s landing face up. The following table shows part of her record.

Suppose Joslyn could roll the die 10,000 times and keep a record of the total number of 5s landing face up in the 10,000 rolls. What would such a record illustrate?

All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material?

The following table shows the classification of all 51 dogs from an animal shelter by whether the dogs lived mostly outdoors or mostly indoors before coming to the shelter and whether they tested positive or negative for a certain skin condition.

One dog from the animal shelter will be selected at random. Based on the table, which of the following statements is correct?

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?

At a small company, 40 percent of the employees are classified as junior level, and 32 percent of the employees work in department A. Of those classified as junior level, 55 percent work in department A. One employee will be selected at random.

What is the probability that the selected employee works in department A and is not classified as junior level?

The table shows the responses from 103 people when asked if they support a proposal to expand the public library.

One person from those who responded will be selected at random. Which of the following is closest to the probability that the person selected will be someone who responded no, given that the person selected is age 55 or older?

The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?

A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?

A contestant’s final winnings on a game show are determined by a random selection of a base amount and a possible multiplier. For the base amount, the contestant randomly selects one of four cards, where two cards are marked $1,000, one card is marked $2,000, and one card is marked $5,000. After choosing the card, the contestant randomly selects one of five chips, where three chips are red and two chips are white. If the selected chip is red, the contestant’s final winnings are twice the value of the base amount. If the selected chip is white, the contestant’s final winnings are the value of the base amount. What is the probability that a contestant’s final winnings are exactly $2,000?

A police officer is using a radar device to check motorists’ speeds. Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. Assuming that the police officer’s estimate is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?

According to a report for veterinarians in the United States, 36.5 percent of households in the United States own dogs and 30.4 percent of households in the United States own cats. If one household in the United States is selected at random, what is the probability that the selected household will own a dog or a cat?