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.

²Pushed 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.

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?
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)?
Calculate the mean, median, and mode for the total murders in the top 20 states.
Calculate the standard deviation and variance for the total murders in the top 20 states.
In Texas, given that a specific person was murdered by a firearm, what is the probability that the murder was committed with a rifle?
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?
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.
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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