Accelerated Geometry Unit 4 Test
Name ______________________________
1. The two-way frequency table shows data from a survey of students enrolled in science classes at Einstein College.
a. Based on the model, how much more likely is it that a student chosen at random would be enrolled in General
Science or Physics than Chemistry? Show your work and explain your answer.
b. Using the data from the model, estimate the probability that a randomly selected student would be enrolled in
Biology given that the student is in the 9th grade. Show your work and explain your answer.
c. According to the model, are the probability of a student enrolled in Chemistry and the probability of a student
enrolled in 12th grade independent of each other? Justify your answer by explaining your work.
2. This Venn diagram shows the names of students in Mr. Leary’s class that own bicycles and skateboards. Let set B be
the names of students who own bicycles, and let set S be the names of students who own skateboards.
a. Find 𝐵 ∩ 𝑆. What does the set represent?
b. Find 𝐵 ∪ 𝑆. What does the set represent?
c. Find (𝐵 ∪ 𝑆)′. What does the set represent?
d. Find 𝐵 ∩ 𝑆. What does the set represent?
3. Assume that the following events are independent:
- The probability that a high school senior will go to college is 0.72.
- The probability that a high school senior will live on campus, given that the person will go to college is 0.64
What is the probability that a high school senior will go to college and live on campus?
4. Nolan has a number cube with sides labeled 1 through 6. He rolls the number cube twice.
a. What is the probability that the sum of the two rolls is a prime number, given that at least one of the rolls is a 3?
b. What is the probability that the sum of the two rolls is a prime number or at least one of the rolls is a 3?
5. The total number of full-time and part-time employees at a store is 50. Each employee works either the morning shift
or afternoon shift. More information about the employees is given below.
 15 employees are part-time
 28 employees are males
 30 employees work the morning shift
 6 male employees work part-time
 12 male employees work the morning shift
The names of each of the 50 employees are written on separate cards. The cards are shuffled and placed into a
container.
a. If one card is selected at random from all 50 cards in the container, what is the probability that the employee is
part-time or male? Show your work.
b. If one card is selected at random from all 50 cards in the container, what is the probability that the employee is
male or works the afternoon shift? Show your work.
c. If one card is selected at random from all 50 cards in the container, what is the probability that the employee is
a female who does not work the morning shift? Show your work and explain your answer.
6. Each letter of the alphabet is written on a card using a red ink pen and placed in a container. Each letter of the
alphabet is also written on a card using a black ink pen and placed in the container.
a. If a single card is drawn at random from the container, what is the probability that the card has a letter written
in black ink, is the letter A, or is the letter Z? Show your work or explain your answer.
b. If two cards are drawn at random from the container without replacement, what is the probability that you
draw a consonant written in red ink and then a vowel? Show your work or explain your answer.
7. A theater on a college campus has 618 audience seats on two levels. The diagram shows the seating chart and the
number of seats in the left, center, and right sections of each level.
All seats are filled for a charity event and a raffle is held to award prizes. All tickets are placed into a large bin and mixed.
a. One ticket is selected at random from the bin. If the selected ticket is known to be a center section ticket, what
is the probability that is from the balcony? Show your work and explain your answer.
b. One ticket is selected at random from the bin. If it is known that the selected ticket is NOT from the left section
of the theater, what is the probability that is from the right section? Show your work and explain your answer.
8. At the end of the school year, all juniors and sophomores in the orchestra were asked whether they would be
attending the summer music camp. The table shows their responses.
One student from the entire group is selected at random. Two events of interest are defined.
a. What is 𝑃(𝑆)? What is 𝑃(𝑌)? Show your work and state your answer in decimal form.
b. What is 𝑃(𝑆|𝑌)? What is 𝑃(𝑌|𝑆)? Show your work and state your answer in decimal form.
c. Based on your answers to part (a) and part (b), are S and Y independent events? Explain your answer.
d. Interpret your answer to part (c) in terms of the students attending the summer music camp.