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2. The table below identies a group of Brooklyn College students by one of four majors and by home state' Use proper probability notation throughout parts (b) - (g). Psychology Mathematics Communication 50 Totals ' (7 points) ' (3 points) ' (3 points) from NV? . (4 points) from NY? . 14 points) 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 What is the probability that a randomly selected student is from NJ, given that he or she is a Psychology major? (4 points) IfC is the event ofa student majoring in Communications, nd the probability of the complement of C. , (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 nds 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 ora cat. b. (4 points) Find the probability that a resident has NEITHER ofthese two pets. Preview File Edit View Go Tools Window Help NO D ) 40% [ : Tue 2:30 PM Q DE 1501 Project 3 (1).pdf (page 1 of 3) ~ Q Search 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.) a. (4 points) P(G and R) = b. (4 points) P(B and (B or G)) = c. (4 points) P(R and G') = d. (6 points) P((G and G) OR (B and R) ) = e. (4 points) Are the two draws independent events? Justify your answer numerically