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Mathematics 3 Pages

Counting Techniques And Introduction To Probability

Question

Counting Techniques and Introduction to Probability 

State
Total murders1
Total firearms
Handguns
Rifles
Shotguns
Firearms (type unknown)
Knives or cutting instruments
Other weapons
Hands, fists, feet, etc.2
Alaska
29
16
5
0
3
8
6
5
2
Arizona
339
222
165
14
9
34
49
59
9
Arkansas
153
110
52
4
6
48
22
17
4
California
1,790
1,220
866
45
50
259
261
208
101
Colorado
147
73
39
3
5
26
22
31
21
Connecticut
128
94
54
1
1
38
18
10
6
Delaware
41
28
18
0
3
7
8
2
3
District of Columbia
108
77
37
0
1
39
21
9
1
Georgia
522
370
326
16
16
12
61
83
8
Hawaii
7
1
0
1
0
0
2
1
3
Idaho
32
17
15
1
0
1
4
8
3
Illinois3
452
377
364
1
5
7
29
29
17
Indiana
284
183
115
9
12
47
36
43
22
Iowa
44
19
7
0
2
10
10
10
5
Kansas
110
73
31
3
5
34
11
16
10
Kentucky
150
100
77
6
5
12
13
24
13
Louisiana
485
402
372
10
8
12
28
29
26
Maine
25
12
3
1
1
7
4
7
2
Maryland
398
272
262
2
5
3
75
34
17
Massachusetts
183
122
52
0
1
69
30
22
9
Michigan
613
450
267
29
15
139
43
89
31
Minnesota
70
43
36
3
3
1
12
12
3
Mississippi
187
138
121
6
4
7
26
14
9
Missouri
364
276
158
13
9
96
28
42
18
Montana
18
7
2
3
1
1
4
5
2
Nebraska
65
42
35
2
1
4
7
9
7
Nevada
129
75
46
2
1
26
20
25
9
New Hampshire
16
6
1
2
1
2
4
6
0
New Jersey
379
269
238
1
5
25
51
41
18
New Mexico
121
60
45
2
2
11
21
32
8
New York
774
445
394
5
16
30
160
143
26
North Carolina
489
335
235
26
19
55
60
57
37
North Dakota
12
6
3
0
0
3
4
0
2
Ohio
488
344
187
8
13
136
44
80
20
Oklahoma
204
131
99
8
9
15
26
21
26
Oregon
77
40
13
1
2
24
22
10
5
Pennsylvania
636
470
379
8
19
64
73
66
27
Rhode Island
14
5
1
0
0
4
5
4
0
South Carolina
319
223
126
10
12
75
38
40
18
South Dakota
15
5
3
1
0
1
4
3
3
Tennessee
373
244
172
7
13
52
51
62
16
Texas
1,089
699
497
37
48
117
175
134
81
Utah
51
26
15
4
1
6
5
9
11
Vermont
8
4
2
0
0
2
2
2
0
Virginia
303
208
110
10
15
73
33
41
21
Washington
161
79
58
1
3
17
29
36
17
West Virginia
74
43
23
10
3
7
11
13
7
Wisconsin
135
80
60
7
3
10
21
13
21
Wyoming
15
11
7
0
0
4
0
1
3
Virgin Islands
38
31
27
0
0
4
5
2
0

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

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.

  1. 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?
  2. 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)?
  3. Calculate the mean, median, and mode for the total murders in the top 20 states.
  4. Calculate the standard deviation and variance for the total murders in the top 20 states.
  5. In Texas, given that a specific person was murdered by a firearm, what is the probability that the murder was committed with a rifle?
  6. 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?
  7. 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.
  8. For what reasons do you think California and Texas seemingly had a disproportionate number of murders than New York and Pennsylvania in 2011?
Solution

Title: Counting Techniques And Introduction To Probability
Length: 3 pages (950 Words)
Style: MLA

Preview

1. 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? 

When ordered is considered: 10P5 

When order isn’t considered: 10P5= =

2. 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)? 

= = 6 x 5 x 4 = 120

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