# MATH 125 Unit 4 Individual ProjectAnswer Form Counting Techniques and Introduction to Probability

NAME: Mary Smith

MATH125: Unit 4 Individual Project

 ANSWERS Order is considered 720 Order is NOT considered 120

• In how many ways can 5 states be selected from the top 10 states with the most murders if the order of the 5 statesmatters?
• In how many ways can 5 states be selected from the top 10 states with the most murders if the order of the 5 states does not matter?

10P3=10! / (10-3)! = 10! / 7! = 10*9*8*7! / 7! = 10*9*8= 720

10C3= 10! / (10-3)! * 3! = 10! / 7! * 3! = 10*9*8*7! / 7! * 3*2*1 = 720 / 6 = 120

• 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)?

6P3= 6! / (6! – 3!) = 6! / 3! = 6*5*4*3! /3*2*1 = 6*5*4 = 120

 RANK TOP 20 STATES TOTAL MURDERS 1 California 1,790 2 Texas 1,089 3 New York 774 4 Pennsylvania 636 5 Michigan 613 6 Georgia 522 7 North Carolina 489 8 Ohio 488 9 Louisiana 485 10 Illinois 452 11 Maryland 398 12 New Jersey 379 13 Tennessee 373 14 Missouri 364 15 Arizona 339 16 South Carolina 319 17 Virginia 303 18 Indiana 284 19 Oklahoma 204 20 Mississippi 187
 ANSWERS MEAN 524.4 MEDIAN 425 MODE There is no mode

• Find the top 20 states with the most number of total murders. Then, calculate the mean, median, and mode.

Mean: 1790+1089+774+636+613+522+489+488+485+452+398+379+373+364+339+319+303+284+204+187 / 20 = 10488 / 20 =524.4

Median: 452+398 / 2 = 850 / 2 = 425

Mode: For this data set, there is not any reoccurring number, therefore, there is no mode.

 ANSWERS VARIANCE 131480.8 STANDARD DEVIATION 362.6

• Calculate the variance and standard deviation for the top 20 states with the most number of total murders.

• Range: 1790 – 187 = 1603
• Variance: (1790-1603)2+(1089-1603)2+(774-1603)2+(636-1603)2+(613-1603)2+(522-1603)2+(489-1603)2+(488-1603)2+(485-1603)2+(452-1603)2+(398-1603)2+(379+1603)2+(373-1603)2+(364-1603)2+(339-1603)2+(319-1603)2+(303-1603)2+(284-1603)2+(204-1603)2+(187-1603)2 / 20-1= 34969+264196+687241+935089+980100+1168561+1240996+1243225+1249924+1324801+1452025+1498176+1512900+1535121+1597696+1648656+1690000+1739761+1957201+2005056 / 20-1 = 25765694 / 19 = 1356089.16
• Standard Deviation: = 362.6
• In Texas, given that a specific person was murdered by a firearm, what is the probability that the murder was committed with a rifle?

• 4 / 699 = 0.0057
• 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?
 CHOSEN STATES PROBABILITY Alaska 0.31 or 31% Arizona 0.74 or 74%