## Counting Techniques and Introduction to Probability

**MATH125:**** Unit 4 Individual Project**

**Counting Techniques and Introduction to Probability**

StateTotalmurders1TotalfirearmsHandgunsRiflesShotgunsFirearms(typeunknown)Knives orcuttinginstrumentsOtherweaponsHands, fists,feet, etc.2Alaska29165038652Arizona3392221651493449599Arkansas15311052464822174California1,7901,2208664550259261208101Colorado14773393526223121Connecticut1289454113818106Delaware412818037823District of Columbia108773701392191Georgia52237032616161261838Hawaii710100213Idaho321715101483Illinois3452377364157292917Indiana28418311591247364322Iowa44197021010105Kansas11073313534111610Kentucky150100776512132413Louisiana48540237210812282926Maine25123117472Maryland398272262253753417Massachusetts18312252016930229Michigan6134502672915139438931Minnesota70433633112123Mississippi18713812164726149Missouri36427615813996284218Montana1872311452Nebraska654235214797Nevada1297546212620259New Hampshire1661212460New Jersey3792692381525514118New Mexico1216045221121328New York7744453945163016014326North Carolina489335235261955605737North Dakota1263003402Ohio488344187813136448020Oklahoma204131998915262126Oregon774013122422105Pennsylvania63647037981964736627Rhode Island1451004540South Carolina319223126101275384018South Dakota1553101433Tennessee37324417271352516216Texas1,089699497374811717513481Utah5126154165911Vermont842002220Virginia303208110101573334121Washington16179581317293617West Virginia744323103711137Wisconsin13580607310211321Wyoming15117004013Virgin Islands383127004520 |
---|

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.

Federal Bureau of Investigation. (2011). *Table 20: Murder*. Retrieved from http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/table-20

**Click following link to download this document**

Counting Techniques and Introduction to Probability.docx