The multiplication rule for dependent events quiz

A local pet groomer accepts walk-in customers. From experience, the groomer has determined that the probability that a walk-in customer will get a full-service grooming, which includes a bath and nail trimming, is 0.71. The probability that a walk-in customer will get a haircut for their pet is 0.42. The probability that customers who get the full-service grooming will also ask for a haircut is 0.28. What is the probability that a walk-in customer will ask for both a full-service grooming and a haircut?

(THIS ANSWER IS WRONG) 0.30

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. The professor informs the class that there will be a test next week. What is the probability that a randomly selected student studied if they do not pass the test with a B or higher?

(THIS ANSWER IS WRONG) 0.59

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. What is the probability that a randomly selected customer vacuums their car?

0.25

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. What is the probability that a randomly selected student studies for a test and gets a B or higher?

0.33

In July in Virginia, the temperature can quickly rise above 90 degrees Fahrenheit, which can also lead to thunderstorms. The probability that the temperature will rise above 90 on a randomly chosen day is 0.68, and the probability of thunderstorms is 0.29. If the temperature rises above 90 degrees, the probability of a thunderstorm is 0.56. What is the probability that the temperature rises above 90 degrees and there is a thunderstorm on a randomly chosen day in July?

0.38

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. Which probability is represented by label 3 in the tree diagram?

0.44

Students in Mrs. Barnes's class determined the probability that she will check homework on a randomly chosen day is 0.8. They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9. What is the probability that the students will have their homework checked and take a pop quiz on a randomly chosen day?

0.48

Students in Mrs. Barnes's class determined the probability that she will check homework on a randomly chosen day is 0.42. They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9. The probabilities are displayed in the tree diagram. What is the probability that Mrs. Barnes does not check homework if the students take a pop quiz?

0.67

A medical clinic is randomly selecting two staff members to attend a conference. The clinic employees include 7 nurses, 3 doctors, and 2 office staff. The nurses want to know the probability that both attendees will be nurses. The tree diagram displays the possible outcomes of randomly selecting two staff members. Which staff member is represented by label 1 in the tree diagram?

not nurse

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. Which order is represented by label 1 in the tree diagram?

plain coffee