dscnt: Using percentages 1 in 470 is 0.2%. Using your logic over the next 470 years every existing handgun will be used in a crime. By that logic I guess the repeat offenders (rapists for one) go out and get a new gun for each crime.
Which one of your compatriots has the forum book 'Statistics for Dummys'? you need borrow it.
No, in 470 years not all guns (in existence or having been in existence during that time period) will have been used in a crime, only about 85% of them - and not even that when you eliminate repeat offenders. Rough guess maybe 50% to 66%, at the rate of offending handgun 99.6% per year (yes 99.6%). I believe 99.8% is for long guns, or 'all' guns perhaps. Handguns are used more frequently in crimes.
99.8%, which is 0.998 for our maths of 0.998 raised to 47th power, over 47 years would result:
0.910 = proportion of guns NOT used in crime over 47 years.
99.8%, or 0.998, over 470 years would result: 0.998 ^ 470th power = .998470 = 0.3902
0.3902 = proportion of guns NOT used in a crime over 470 years (of those in existence that time).
Ergo, 100% - 91% = 9% WILL have been used in a crime over 47 years.
100% - 39% = 61% of guns WILL have been used in a crime over 470 years.
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However, remembering, that's for either all guns or long guns. For handguns, the percentage of a handgun being used in a crime is (or was pre heller) 99.6%, which will alter the above resultants.
0.996 raised to 47th power = 0.82830; Ergo, approx 17% of handguns over 47 years, used in a crime.
http://www.endmemo.com/algebra/nthpower.php
0.996 raised to 470th power = 0.1520; Ergo, approx 85% handguns over 470 years, used in a crime.
I guess you weren't that far off, what with 85% probability of a handgun in existence over 470 years, being used in a crime!
But these would include repeat offenders, which muddies up the mix, and lowers the resultants somewhat. Not as much as you'd think tho, since crime guns being recovered would temper even that.
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