Lab I – Probability Models
When finished fill in the table at the end of this document and email it to your teacher
Cards:

Use the tab for Cards in the excel file and get the total probability for the various hands

All of your inputs are on the yellow cells

(a) The first task is to figure how many chances you have for each pick that will result in a successful hand
INPUT: columns B/C/D/E/F

(b) Then if any of the events (one of the five cards) has 100% chance then you need multiply the one path by five to account for the parallel paths to a successful hand
INPUT: column H

(c) Finally, if there are more than one way to get the result (example four of a kind can be done with 13 different cards) then you need to add that number too
INPUT: column J
Note: this step will be more complicated when dealing with royal hands, and multiple runs.

(d) Your final probability will be the percentage in the last column in the “prob” row (I’ve formattesd it such that these all fall in rows 7,17,27, etc)
Dice:

Use the tab for Dice in the excel file and get the probabilities for all the outcomes when tossing three dice

Note: this problem has been started with the first result for the outcomes of 3 and 4

The probability also has been simplified to two events (rather that 3) by using the results from lab H for the rolls for dice #2 and #3… see below (also on your excel file)

Outcome | theoretical % | total | possible outcomes (die 1 / die 2) | 2 | 3% | 1 | 1/1 | | | | | | 3 | 6% | 2 | 1/2 | 2/1 | | | | | 4 | 8% | 3 | 1/3 | 2/2 | 3/1 | | | | 5 | 11% | 4 | 1/4 | 2/3 | 3/2 | 4/1 | | | 6 | 14% | 5 | 1/5 | 2/4 | 3/3 | 4/2 | 5/1 | | 7 | 17% | 6 | 1/6 | 2/5 | 3/4 | 4/3 | 5/2 | 6/1 | 8 | 14% | 5 | 2/6 | 3/5 | 4/4 | 5/3 | 6/2 | | 9 | 11% | 4 | 3/6 | 4/5 | 5/4 | 6/3 | | | 10 | 8% | 3 | 4/6 | 5/5 | 6/4 | | | | 11 | 6% | 2 | 5/6 | 6/5 | | | | | 12 | 3% | 1 | 6/6 | | | | | | | | 36 | 11 | 9 | 7 | 5 | 3 | 1 |

The process for calculating this probability is different that with the cards, because each parallel path is rarely the same, so you are not able to just multiply the same results as you did parts (b) and (c) for the cards

(a) First you need to make copies of the A1:H3 for your first path For example: to get to the result of three dice to be 6, you could roll a 1 on the first roll
(b) Then you need to find the probability of reaching your result (in this case 6) after three dice have been rolled
(1) Change the red x to what your first roll is (in this case 1)
(2) Fill in the yellow cells to show the chance of rolling this first die (in this case 1 out of 6)
(3) Change the red y to what you need your combined roll #2 and #3 to be to reach the result (in this case since your result is to be 6, and your first roll is 1, you need the next two to sum to 5)
(4) Finally fill in the yellow cells for this second event (in this case 4/36)
(c) Now you need to make copies of the A1:G3 for any other successful paths For example: to get to the result of three dice to be 6, you could roll also roll a 2 on the first roll Repeat steps (1) thru (4) for this possibility
Repeat (c) until all successful paths have been put into your model

Finally –you need to add up all your paths into the sum in column H (RED cell in your first row) to add up all the possible paths to get you total probability of getting the result (in this case 6)

After you have finished all outcomes: 3 to 18, you should be able to verify that they all add up to 100%

template on following page – please copy and paste into your final submittal to teacher –
I do not want a copy of these instructions in your submittal!

I. Cards: probability of flush | | probability of four of a kind | | probability of Royal straight flush | | probability of Straight flush | | probability of Royal Straight | | probability of ANY Straight | |
Dice:
Outcome | Probability | 3 | | 4 | | 5 | | 6 | | 7 | | 8 | | 9 | | 10 | | 11 | | 12 | | 13 | | 14 | | 15 | | 16 | | 17 | | 18 | | total | |