The engineers of a certain company are asked to answer the following survey with Y and N selection: A. Is it necessary to modernize the laboratory equipment? B. Is it necessary to build a sport and wellness facility for the company? a. List the possible sample space for this survey for a given engineer. Draw the tree diagram. b. Suppose that out of 40 engineers, 24 answers [Y,Y), 8 answers (Y, N), 6 answers (N, Y), and 2 answers (N, N). Find P (A), P(B), P(C), and P(D), if A is the event that the answer is (Y, Y), B is the event that the answer is ( N,Y), C is the event that the answer is (N, Y), and D is the event that the answer is (N,N). c. What is the probability that, randomly selecting an engineer, he/she would answer Y to the question concerning modernizing the laboratory equipment? Let M be the event of modernizing the laboratory equipment. d. What is the probability that, randomly selecting an engineer, he/she would answer Y to the question concerning the necessity to build a sport and wellness facility for the company? Let B be the event of building a sport and wellness facility for the company. e. What is the probability that, randomly selecting an engineer, he/she would answer Y to the question concerning the modernizing the laboratory equipment or necessity to build a sport and wellness facility for the company? Draw a Venn diagram