The below image shows various subsets of cells of a triangular array. Note that some of the subsets overlap one another in non-empty intersections, while others do not. Given a similar triangular array of cells numbered 1 to 15. identify an exhaustive collection of subsets of cells A, B, C, D of sizes specified in your individualized parameters below, so that your choices result in a non-empty intersection between the pairs of sets given to you in your individualized parameters, but no others. Important tote: It has been discovered that there is a small error in the R- script that generates the parameters below. This occasionally results in size parameters that are impossible to satisfy in combination with the parameters for required intersections. If you discover this is true for your particular parameters, you may change the sites required to 4 numbers of your choosing that allow you to construct the sets in a manner still consistent with your given requirements about intersections (don't forget the sets must also be exhaustive) ID A 15-sided die is rolled to identify a random cell or from 1 to 15. First, calculate the probabilities of each of the following: a. x is in A b.z is in B C is in C d. is in D e. is in A and B c 1. r is in A and D g. I is in A and B and C and D h. given that is in C. is also in D i. given that is in A or Bar is also in C or D Then, calculate the probabilities described below in problems #1-8. This time however, calculate the probability using only previously calculated values. (For example, to find the value for problem 4. you may use any values from problems (a)-CD or #1- #3.) Also, identify which of the probability concepts listed below are used in your calculation. (Note, there may be more than one concept used in any single problem.) {Addition Rule, Multiplication Rule. Complement, Conditional Probability) Finally, answer the two questions posed in #9-10. 1. z is in A or B 2. is in C and D 3. z is either in A and B, or it is in C and D 4. is in A or B, while also being in C or D 5. isn't in A 6.2 is neither in A nor D 7. Given that is in D. it is also in A 8. Given that is in C or D. is also in A or B ar C B 9. Which of the 6 possible pairs of sets A, B, C, and D represent disjoint events? 10. Which of the 6 possible pairs of sets A, B, C, and D represent independent events? Type your answers following the format shown in the example below exactly. Additionally, scan your handwritten work showing your application of the probability concepts mentioned in your answers for #1-8 and upload the scanned file to canvas. When typing your answers, make sure to do the following . Use the hash tag symbol (#) where it appears Use the "c0" as shown to "combine" elements into a set Use capital letters A, B, C, and when identifying your chosen sets Round numerical answers to 4 decimal places Example of Format for Submissions (note, most answers shown are incorrect): A WESTER! * W1234567 these 2.2.3.45 R. 114.5.6.1 2.9.10) D-0.11.12.13, 14.11 er a1 3.3333 003333 Individualized Parameters for Portfolio Submission #1: = * sizes required for A, B, C, and D, respectively 6,5,6,4 * pairs with non-empty intersections = A & C, A & D, B & D
