Math Discrete....!

Contingencies

(c)2016 Second WInd Productions, LLC

(c)2016 Second WInd Productions, LLC

On this worksheet, you are to use the COUNTIFS macro as discussed in PA2.2. You will need to fill in each light-orange-shaded cell (8 total) based on its respective (top, side) header labels. Start by alphabetically sorting the data values (labels) along Columns G and H. Then transfer (by using = signs) each of the Initiating Action labels to the header cells located along Column K, and then the Resulting Action labels to the header cells along Row 5. Next, use COUNTIFS to populate the 8 lightly-shaded violet cells in the body of the table by using the data located along Columns P & Q. Be efficient in how you fill in these cells! BL Opp: Use the array functionality demonstarted in PA2.2 Caution: Do not reorder the data along Columns P & Q. Finish filling in the table's margins, etc., as shown in PA2.2. The issue at hand is there seems to be a series of faults occurring when using a new program, so this is a way to see if we can isolate what is most likely causing the issue, or at least give some indication of what to look for when the issue occurs. Once the table is completed, go to the next worksheet.

Discrete Pr

(c)2016 Second WInd Productions, LLC

(c)2016 Second WInd Productions, LLC

CAUTION You must complete the previous worksheet before performing this one! When you complete the previous worksheet, the table will fill itself out  You are going to fill in the 8 blue-shaded cells along Rows 16-20 based on the values found in their respective cell locations in the first table; the common divisor in each case is the grand total located in Cell P9. BL Opp2 If you can figure it out, use array functionality to fill in the probabilities in the 2nd table Express each probability as a percentage to one decimal place. Then answer these questions as and where indicated: Which initiating action is most probable to cause a fault to occur? Answer Here  Which initiating action is least probable to cause a fault to occur? Answer Here  Which initiating action is least probable to result in a continue response? Answer Here  Which initiating action is most probable to result in a continue response? Answer Here  What is the most probable cause-effect set and what is that probability as found above right, and what is that probability? Cause-Effect Set = Probability =

Set Probabilities

(c)2016 Second WInd Productions, LLC

(c)2016 Second WInd Productions, LLC

Let's use what we have learned to help us define some probabilities. We'll expand some of that work on the next worksheet by using combinatorials. Consider the element list at the right which we have designated as set S.: The first thing we want to do is determine the cardinality, which we will enter in Cell N4 as indicated. This represents our common denominator value when determining our probability values. Display these values to 3 decimal places. We are now ready to define the probabilities as shown at the right. In each case, the numerator value will be determined by using one of the COUNT macros from the PA, while the denominator will be as we stated above, the value is Cell N4. When using a COUNT macro, make sure to select an applicable cell value in the enclosed blue-shaded region along Columns R-T (do NOT type in any values). When you are done here, proceed to the next worksheet.

nCr

(c)2016 Second WInd Productions, LLC

(c)2016 Second WInd Productions, LLC

Do you recall how we determine the cardinality of a Power Set, P(S), of any set of n items? Well, here's another way of determining the values, which we'll use to help us with the stuff at the right    So, let's now implement this. Enter the following into Cell N3: =COMBIN($M$15,M3) Reselect Cell N3 and copy its contents down to the bottom of the list. Then enter into Cell P3 the sum of the values you just calculated along Column N. Cell P3 defines | P(S) |  | S | = 12. Let's now make some probabilities. Start by setting your responses to display three decimal places along Column T. Meanwhile, Cell P3 will serve as our value for our denominators. So, Cell T3 is asking what is the probability of selecting a random subset of S and having it have a cardinality of 2. Clearly, this would equal the value in Cell N5 divided by the value in P3. Similar for the rest (note: Hex refers to 6 and Hep refers to 7). In contrast, the value for Cell T17 is asking for a specific triplet sequence, of which there can be only one (reminds me of Highlander . . . ). So, T17 is simply 1 (CAUTION: This is selectable on the worksheet!) divided by the cardinality of the power set. This is as opposed to the next question which now narrows the deniminator down to just the total number of triplets; we now divide instead by the value in Cell T6. Cool. I'll let you ponder, and answer, Cell T21. Hint: It's a value that you COULD just type ... but it is also, again, selectable on the worksheet, so select, do not just type in . . . Next worksheet . . .

Floor Ceiling

Let's explore how to use Excel's rounding functions to achieve the Floor and Ceiling functions. We will do this by employing the ROUNDDOWN and ROUNDUP macros, respectively, In each case, we will define the number of decimals to which we are rounding as being 0; this ensures that we get integer results. In Cell M3, enter =ROUNDDOWN(L3,0) In Cell N3, enter =ROUNDUP(L3,0) In Cell O3, enter =INT(L3) Select Cells M3-O3 and drag down to Row 16 (FALSE along Column L)