Unit 3 Probability

A lottery game contains 24 balls numbered 1 through 24. What is the probability of choosing a ball numbered 25?

A. 0

A jar contains 7 red jelly beans, 2 black jelly beans and 6 green jelly beans. You draw ONE jelly bean. What is the probability of drawing a red bean?

A. 7/15

An online news report claims that 50% of online news readers work in the business industry. To test this claim, a researcher takes an SRS of 25 online news readers. Nine of them work in the business industry. A simulation of 65 trials was conducted under the assumption that 50% of online news readers really do work in the business industry. Based on this dotplot and the sample of 25 online news readers, which conclusion can be drawn?

There is about a 0.046 chance that 9 or fewer online readers work in the business industry. This is unusual and is convincing evidence that less than 50% of online readers work in the business industry.

A fitness expert claims that 25% of adults do not know how to swim. To test this claim, an SRS of 20 adults is taken. Two of the adults do not know how to swim. A simulation of 100 trials is conducted based on the assumption that 25% is the true probability that an adult does not know how to swim. Based on the dotplot of the simulation results and the sample of 20 adults, which conclusion can be made?

There is about a 12% chance of 2 or fewer nonswimmers in a group of 20. This is not unusual and is not convincing evidence that the true probability that an adult cannot swim is less than 25%.

A large city's transit department claims that only 10% of city buses run off schedule. To test this claim, a random sample of 10 buses is chosen at random. Five of the buses are running off schedule. To see how unusual this sample of buses is, a simulation of 100 trials was conducted under the assumption that 10% of the buses run off schedule. Based on the dotplot of the simulation results and the sample of 10 buses, which conclusion can be drawn?

There is about a 3% chance that 5 or more buses are running off schedule. This is unusual and is convincing evidence that the true probability that a bus is off schedule is more than 10%.

A deli owner made a probability distribution chart for the meat choices of their customers' sandwiches when the sandwiches contain only one meat. What is the missing probability in the table?

0.09

A study reports that about half of pet owners have either a dog or a cat. The other half of pet owners have birds, reptiles, or other animals. To find out if this applies in its area, an animal shelter surveys a random sample of 30 pet owners. Nineteen of them say they own either a cat or a dog. Let even digits represent owning a cat or a dog and odd digits represent owning some other type of animal. Using the line of random numbers, what is the best estimate of the proportion of responses in a sample who own either a cat or a dog?

0.53

Sports science researchers determined that, for those people who skateboard, 22% have never had an injury, 45% have had one injury, 18% have had two injuries, and 15% have had three or more injuries. What is the probability that a randomly chosen skateboarder has had one or two injuries?

0.63

A group of ticket takers at a box office for a new theater noticed that in the first year of the theater's operation, the genre breakdown of the movies was 10% horror, 39% comedy, 28% drama, and 23% action. If a movie from the theater's first year of operation was selected at random, which of the following identifies the probability distribution for the movie's genre?

B.

Some college advisors noticed the following breakdown of majors for the incoming freshman at their school: 3% math, 22% nursing, 16% psychology, 11% criminal justice, and 48% business. Suppose a first-year student was chosen at random. Which of the following is the probability distribution for that student's major?

B.

Three siblings, Peyton, Cameron, and Dakota, all ask their parents to borrow the family car for different events around town. Since they cannot all borrow the car at the same time, the parents decide to use randomness to decide who gets the car. They will roll a single, fair, six-sided number cube. Peyton gets the car if a 1 or 2 is rolled. Cameron gets the car if a 3 or 4 is rolled, and Dakota gets the car if a 5 or 6 is rolled. Which of the following is the probability distribution for who gets the car?

B.

A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 8).

B. 2/13

The partially filled contingency table gives the frequencies of the data on age (in years) and sex from the residents of a retirement home. What is the relative frequency for males ?

C. 5/8

A class consists of 63 women and 86 men. If a student is randomly selected, what is the probability that the student is a woman?

C. 63/149

A group of marketing researchers for a popular cell phone manufacturer collected the following information about young adults (aged 18-25): 1% use a cell phone that is 3 years or older, 2% use a cell phone that is 2-3 years old, 20% use a cell phone that is 1-2 years old, and 77% use a cell phone that is less than 1 year old. Suppose a young adult was selected at random. Let X equal the age of a randomly selected person's cell phone. Which of the following is the probability distribution for the age of that person's cell phone?

D.

A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue). Please select the best answer from the choices provided

D. 3/4

A lottery game has balls numbered 1 through 15. What is the probability of selecting an even numbered ball or the number 12 ball?

D. 7/15

A manufacturer of baseball hats claims that approximately 30% of people regularly wear baseball hats. From a random sample of 20 students at your school, you find that only four wear baseball hats regularly. This gives you reason to believe that the manufacturer's claim of 30% is too high. Let the digits 0-2 represent wearing a baseball hat (H) and the digits 3-9 represent not wearing a baseball hat (N). Use the table of random numbers to run one trial of this simulation. Which is the correct sequence of outcomes?

NNNNN HHNNN NNNHN NHNHN

A teacher claims that there is a 50% chance that she will collect homework for a grade on any given day. One week, she collected all five daily homework assignments. A student in this class is upset and explains that the teacher should not collect any homework assignments the following week in order to honor her 50% probability claim. Is the student's reasoning correct?

No, collecting homework and not collecting homework are equally likely in the long run, so whether or not the teacher collects homework on any single day cannot be determined.

Shamir loves watching professional basketball. His favorite player, Freddy Rocket, successfully completes 85% of his free throws. During one game, Rocket misses his first four free throws. Shamir says that the next free throw has to be a success since Rocket rarely misses so many in a row. Is Shamir's reasoning correct?

No, the probability of Rocket making a free throw is 0.85 over the long run.

Reese, Greg, and Brad meet once a week for coffee. They each have their favorite café and, to be fair, they use randomization to choose where they will meet. Each person has a colored marble: red (R) for Reese, green (G) for Greg, and blue (B) for Brad. Each week, all three marbles are mixed well in a bag and a marble is selected. The favorite café of the person associated with the selected marble is chosen for that week's meeting. Which of the following represents the sample space for choosing a café for the first two weeks?

R & R, R & G, R & B, G & R, G & G, G & B, B & R, B & G, B & B

A contractor claims that she finishes a job on time 90% of the time. Last month, she only completed 7 out of her 10 jobs on time. To see if this is surprisingly low, a simulation was conducted 100 times under the assumption that she really does complete 90% of her jobs on time. The dotplot contains 100 trials of this simulation. Based on this dotplot and the sample of last month's on-time completions, which conclusion can be drawn?

The dotplot does not provide convincing evidence that her true, on-time completion rate is less than 90% because 7 or fewer on-time completions happened 19% of the time in the simulation.