a- Use the given probabilities to construct a hypothetical 1000 table with columns corresponding to whether or not a student prepared properly for their final exams and rows corresponding to whether the student passes the course or not. b- Use the table to calculate the following probabilities i. The probability of preparing for the final exam or passing the course. ii. The probability of not preparing for the final exam nor passing the course. c- Are the events P(P) and P(S) independent? Justify your answer. d- Are the events P(P) and P(not S) mutually exclusive? Justify your answer.

3. 01:26:35 The following two-way table shows the distribution of daily traffic and weather issues in a certain large city. Suppose a day from this city is selected at random. Let event A = heavy traffic and event B = bad weather. Are events A and B independent? Daily Traffic No, P(A) = P(B|A). Нeavy Traffic Light Traffic Total O No, P(A) + P(A|B). O Yes, P(A) = P(A|B). O Yes, P(A) + P(B|A). Bad Weather 25 30 Good Weather 55 15 75 Total 80 20 100 Weather Conditions

A student takes a multiple-choice quiz with 5 questions, each with four possible answers and only oneof them is correct. A passing grade is 60% or better (i.e., answering at least 3 of 5 questions correctly).Suppose that the student was unable to find time to study for the exam and just guesses at eachquestion.  Find the probabilities for the two events below.i. the student gets exactly 3 questions correct.ii. the student passes the exam

In an inspection of automobiles in a certain Country, 60% of all automobiles had emissions that did not meet EPA regulations. For a random sample of 10 automobiles, compute the following probabilities: a. All 10 automobiles failed the inspection. b. Exactly 6 of the 10 failed the inspection. c. Six or more failed the inspection. d. All 10 passed the inspection.

At the beginning of each day, a patient in the hospital is classifed into one of the three conditions: good, fair or critical. At the beginning of the next day, the patient will either still be in the hospital and be in good, fair or critical condition or will be discharged in one of three conditions: improved, unimproved, or dead. The transistion probabilities for this situation are                                         Good    Fair    Critical                        Good         0.65     0.20    0.05                        Fair            0.50     0.30     0.12                        Critical       0.51     0.25     0.20               Improved       Unimproved         Dead Good       0.06               0.03                    0.01 Fair          0.03               0.02                    0.03 Critical     0.01               0.01                    0.02   For example a patient who begins the day in fair condition has a 12% chance of being in critical condition the next day and a 3%…

A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth. Male Female Passed P(male) = 28 14 Since P(male | pass) = so the events are Submit Answer Failed 18 9 and the two results are attemnt 1 of 2

4. 60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation – e.g., P(A|B) =..) a. Draw a tree diagram to model the problem b. What is the probability that a randomly selected home has a sprinkler system? c. What is the probability that a randomly selected home with a sprinkler system has a lawn service? d. What is the probability that a randomly selected home with a lawn service has a sprinkler system? e. What is the probability that a randomly selected home has a lawn service? f. What is the probability that a randomly selected home that does not have a lawn service has a sprinkler system?

students, 59% attend four-year institutions, and the attend two-year institutions. Males make up 44% of the students in the four-year institutions and 40% of the students in the two-year institutions. (a) Find the four probabilities for each combination of sex and type of institution in the following table. Be sure that your probabilities sum to 1. Male Female Four-year institution Two-year institution noilalugeg blo