# Counting Techniques and Introduction to Probability

MATH125: Unit 4 Individual Project

Counting Techniques and Introduction to Probability

1 Total number of murders for which supplemental homicide data were received.

2 Pushed is included in hands, fists, feet, etc.

3 Limited supplemental homicide data were received.

(FBI, 2011)

The table above for murders by weapon types is from the FBI’s Criminal Justice Services Division and represents the reported murders in each state for the year 2011. (Please see http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/table-20 for the referenced table.)

Be sure to show ALL of your work details. Submit your answers in a Word document in the Unit 4 IP Submissions area.

 Mississippi 187 -337.4 113,838.76 Oklahoma 204 -320.4 102,656.16 Indiana 284 -240.4 57,792.16 Virginia 303 -221.4 49,017.96 South Carolina 319 -205.4 42,189.16 Arizona 339 -185.4 34,373.16 Missouri 364 -160.4 25,728.16 Tennessee 373 -151.4 22,921.96 New Jersey 379 -145.4 21,141.16 Maryland 398 -126.4 15,976.96 Illinois 452 -72.4 5,241.76 Louisiana 485 -39.4 1,552.36 Ohio 488 -36.4 1,324.96 North Carolina 489 -35.4 1,253.16 Georgia 522 -2.4 5.76 Michigan 613 88.6 7,849.96 Pennsylvania 636 111.6 12,454.56 New York 774 249.6 62,300.16 Texas 1,089 564.6 308,610.36 California 1,790 1,265.6 1,601,743.36

Reference

• How many ways are there for choosing 5 states from the top 10 states with the most murders if order is considered? What about if order is not considered?
• Order matters: 10P5 = 30,240
• 10-5=5 10x9x8x7x6x5x4x3x2x1/5x4x3x2x1= or 10x9x8x7x6= 30,240
• Order doesn’t matter: 10C5 = 252
• 10-5=5 10x9x8x7x6x5x4x3x2x1/(5x4x3x2x1)(5x4x3x2x1) or 3628800/(120×120) = 252
• What would be the probability that randomly choosing 3 states from the top 6 murder states would actually be the top 3 states for murders in the United States in exact correct decreasing order (1. CA, 2. TX, 3. NY)?
• Order matters: 6P3 = 120
• 6-3 =3 6x5x4x3x2x1/3x2x1 or 6x5x4 = 120
• Calculate the mean, median, and mode for the total murders in the top 20 states.
• Top 20 Murder totals & States: x – Mean: ^2:
• Mean: 524.4 (add all of the numbers up = 10,215/20 = 524.4)
• Mode: There is no mode
• Median: 425 (Illinois + Maryland = 850 / 2 = 425)
• Calculate the standard deviation and variance for the total murders in the top 20 states.
• Variance: 130,945.89 (total from 20 states = 2,487,972 / 20 – 1 = 19)
• Standard Deviation: = 361.86
• In Texas, given that a specific person was murdered by a firearm, what is the probability that the murder was committed with a rifle? 699 (total firearm murders) & 37 (total rifle murders)
• 37/699 = 0.0529 = 5.29%
• In California, given that a specific person was murdered by a firearm, what is the probability that the murder was committed either with a rifle or a shotgun?
• 1,220 (total firearm murders) & 45 (total rifle murders) & 50 (total shotgun murders)
• 50 + 45 = 95/1,220 = 0.0778 = 7.78%
• Choose 2 states, and determine how much more likely a person is to be murdered using a handgun in one state than the other if the person is murdered.
• Michigan handgun murders: 267 (total murders: 613) New York handgun murders: 394 (total murders: 774)
• 267/613 = 0.435 394/774 = 0.509
• = 72.2%
• For what reasons do you think California and Texas seemingly had a disproportionate number of murders than New York and Pennsylvania in 2011? I think the reason the four states were so different is because Texas and California are both larger than New York and Pennsylvania, also people expect New York and Pennsylvania to have a lot of murders so law enforcement pays more attention.