MATH 1501 PROJECT 3 NAME ____________________________________

INSTRUCTIONS: You may not seek help from the Learning Center, another person or the internet. You can write your solutions on this project or on a different piece of paper. This project is due Wednesday March 24 at 12:50 pm. Answers with little to no work may result in little to no credit. You will scan your project and submit it to Blackboard to the Project 3 portion of the "Projects" page.

THROUGHOUT THE PROJECT, ROUND DECIMALS TO 3 PLACES.

1. Suppose that you have 30 marbles in a bag, 12 are blue, 10 are green, and 8 are red. You randomly draw two marbles, one at a time, without replacement.

• B = marble drawn is blue
• G = marble drawn is green
• R = marble drawn is red
• Calculate the following probabilities. (Each probability is unique. Meaning that after part a is done, all marbles go back in the bag and you draw for part b from the full bag.)

1. (4 points)
2. (4 points)
3. (4 points)
4. (6points)
5. (4 points)

P(GandR)=

P(Band(BorG))=

P(R and G') =

P((GandG)OR(BandR))=

Are the two draws independent events? Justify your answer numerically.

2. The table below identifies a group of Brooklyn College students by one of four majors and by home state.

Use proper probability notation throughout parts (b) - (g).

Home State

Psychology

Mathematics

Communication

Music

Totals

NJ

50

95

250

NY

75

40

Totals

95

115

465

1. (7 points)
2. (3 points)
3. (3 points) from NY?
4. (4 points) from NY?

Complete the table.

What is the probability that a randomly selected student is a Music major?

What is the probability that a randomly selected student is a Communication major

What is the probability that a randomly selected student is either a Mathematics or

e. (4 points)

is a Psychology major?

What is the probability that a randomly selected student is from NJ, given that he or she

1. (4 points) If C is the event of a student majoring in Communications, find the probability of the complement of C.
2. (2 points) In words, what does the complement of C represent?

3. In an apartment building, 55% of the residents have a dog and 30% of residents have a cat. The landlord finds that 15% have both a dog and a cat. Let D be the event that a resident has a dog and let C be the event the resident has a cat.

a. (4 points) Find the probability that a resident has a dog or a cat.

b. (4 points) Find the probability that a resident has NEITHER of these two pets.