Probability Unit Test Review

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. The gym coach randomly selects a student. Assuming the probabilities of selecting a student who can do fewer than 14 pushups and selecting a student who can do more than 45 pushups are the same, what is the value of the missing probabilities? A. 0.07 B. 0.14 C. 0.25 D. 0.33

A. 0.07

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? A. 0.114 B. 0.131 C. 0.686 D. 0.784

A. 0.114

A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console, and 50 brought neither a microwave nor game console. A survey participant is randomly selected. Let M be the event the participant brought a microwave and let C be the event the participant brought a video game console. Organize these events in a two-way table. What is the probability that the participant did not bring a microwave or did not bring a console, P(MC or CC)? A. 0.10 B. 0.29 C. 0.39 D. 0.90

B. 0.29

Four girls and six boys are in a Spanish club. Three of the people will be chosen at random to represent the group in a photograph. What is the probability that one girl and two boys will be chosen? A. 40% B. 50% C. 60% D. 70%

B.50%

A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Two marbles are drawn from the bag. Which expression represents the probability that one of the marbles is red and the other is blue? A. (30P2)/(50P2) B. (30C2)(50C2) C. (10C1)(20C1)/(50C2) D. (10P1)(20P1)/(50P2)

C. (10C1)(20C1)/(50C2)

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? A. (1/12)³ B. (2/12)³ C. (3/12)³ D. (10/12)³

C. (3/12)³

A three-digit personal identification number is chosen using the digits 1-9. The digits cannot be repeated. What is the approximate probability that the first digit will be 6? A. 0.00595 B. 0.03571 C. 0.11111 D. 0.66667

C. 0.11111

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives. What is the approximate probability that a student chooses a computer elective and an art elective? A. 0.11364 B. 0.21212 C. 0.22727 D. 0.42424

C. 0.22727

A recent survey found that 80% of jeans have back pockets, 65% have front pockets, and 48% have both back and front pockets. Suppose a pair of jeans is selected at random and it is determined that it has front pockets. What is the probability that a randomly selected pair of jeans with front pockets also has back pockets? A. 0.52 B. 0.60 C. 0.74 D. 0.81

C. 0.74

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. 0 B. 2/3 C. 4/9 D. 1/2

C. 4/9

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). Using the table of random numbers provided, which gives the correct sequence of students in a simulated sample who have flown at least once (F) and who have not flown at least once (N)? A. FFFFN FFNNF FFFNN FFFFN B. FNNNN NFNFF FFFNN FFFNN C. FNNFN FFNFF FFFFF FFFFF D. NFFNF NNFNN NNNNN NNNNN

C. FNNFN FFNFF FFFFF FFFFF

A certain dog can catch a properly thrown tennis ball with a probability of 0.95. Unfortunately, this dog has dropped the last six properly thrown tennis balls. The owner explains that the next throw has to be caught by the dog because he never misses this many. Is the owner's reasoning correct? A. No, the dog is on a losing streak, so he will drop the next ball thrown. B. Yes, the dog has missed the last six properly thrown tennis balls, so the next one thrown will be caught. C. No, the probability of the dog catching a properly thrown tennis ball is 0.95 over the long run, so the owner cannot say what will happen on the next throw. D. Yes, the dog catches 95% of properly thrown tennis balls, so the next one must be caught to compensate for the previous misses.

C. No, the probability of the dog catching a properly thrown tennis ball is 0.95 over the long run, so the owner cannot say what will happen on the next throw.

The following two-way table shows the distribution of a random sample of travelers and their preferences for accommodations and method of travel. Suppose a traveler is selected from this sample at random. Let event A = home sharing and event B = fly. Are events A and B independent? A. No, P(A) = P(A|B). B. No, P(A) ≠ P(B|A). C. Yes, P(A) = P(A|B). D. Yes, P(A) ≠ P(B|A).

C. Yes, P(A) = P(A|B).

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 purchases the ultimate car wash if they vacuum their car? A. 0.12 B. 0.20 C. 0.32 D. 0.48

D. 0.48 1. Find the probability for vacuuming. (0.45 x 0.10 = 0.045, 0.35 x 0.25 = 0.0875, 0.20 x 0.60 = 0.12, 0.045 + 0.0875 + 0.12 = 0.2525) 2. Find the probability of the customer choosing ultimate and vacuuming. 3. Divide the ultimate and vacuuming by all probabilities of vacuuming.

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? A. Josie's mom is calling her 80% of the day. B. If Josie is doing 10 important tasks in one day, her mom will call during 8 of those tasks. C. Josie has an 80% chance of completing her important tasks without her mom calling her. D. Over the course of many weeks, about 80% of the calls from Josie's' mom will come when she is busy doing important tasks.

D. Over the course of many weeks, about 80% of the calls from Josie's' mom will come when she is busy doing important tasks.