Unit Test — Unit test Answers

At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram.

An airline claims that 80% of adults have flown at least once. From a sample of 20 teenagers it is found that only 13 have flown at least once, giving reason to believe that the true parameter for teens is less than 80%.Let 0–7 represent having flown at least once (F) and let 8–9 represent never having flown (N).

The following two-way table shows the distribution of weekend work hours and how long employees have been at the company.

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. What is the probability that Greg will not get to pick the café for either of the first two weeks?

A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram.

In a certain board game, a 12-sided number cube showing numbers 1–12 is rolled. If 4 such number cubes are rolled, what is the probability that at least 1 number cube will show a number 8 or larger?

In a certain board game, a 12-sided number cube showing numbers 1–12 is rolled. If three such number cubes are rolled, what is the probability that all three show a number 10 or larger?

There are 22 participants in a spelling bee. In how many ways can the top 5 participants finish? Use the formula for permutations to find your answer.

Josie believes that her mom calls her at the most inconvenient times. As a matter of fact, Josie thinks that 80% of the times that her mom calls, she is busy doing important tasks such as schoolwork, driving, or feeding the family pets.Which is the best interpretation of this probability?

At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. The tree diagram displays the possible outcomes of orders at this coffee shop.

For students majoring in Hospitality Management, it was determined that 5% have visited 1–10 states, 16% have visited 11–20 states, 45% have visited 21–30 states, 19% have visited 31–40 states, and 15% have visited 41–50 states. Suppose a Hospitality Management student is randomly picked. What is the probability that the student has visited 30 or fewer states?

How many 2-letter combinations can be created from the distinct letters in the word “mathematician”? Assume that the order of the letters does not matter.

At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. What is the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item?

A librarian has 10 nonfiction and eight fiction books from which to choose the next three book club selections.What is the approximate probability that she chooses a fiction book, then a nonfiction book, then a fiction book?

Students were given a fitness test in gym class, and were required to perform push-ups for two minutes. The assignment of probabilities for the different outcomes is shown in the table.# of push-ups 45Probability?0.740.12?