Frequency distribution of coins - Gambling and Probability

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Frequency distribution of coins

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07-10-2017 , 04:36 PM

PLBlow

grinder

Join Date: Sep 2011 Posts: 445

Lets say that I have collected the change from all cash purchases I have made over the last 10 years and put the change in a giant jar.

What will be the distribution of pennies, dimes, nickles and quarters (%)

im guessing pennies>quarters>nickles=dimes

is there a way to answer this question exactly?

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07-10-2017 , 09:48 PM

akkopower1

centurion

Join Date: Feb 2017 Posts: 198

Coins shipped by the US Mint 1990-2000, the averages to the
nearest 0.25%

1c - 66.5%,
5c - 8.25%,
10c - 13.25%,
25c - 12%

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07-10-2017 , 10:24 PM

Didace

Carpal \'Tunnel

Join Date: Nov 2009 Posts: 19,866

Assume that your change for purchases is evenly distributed form .01 to .99 (true?) and that you always received the change in the fewest coins possible - You get pennies for every amount that doesn't end in a 0 or 5 so I would guess that is the most. It wouldn't be that hard to do a count of all the combos and see.

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07-10-2017 , 10:45 PM

PLBlow

grinder

Join Date: Sep 2011 Posts: 445

Quote:

Originally Posted by Didace

Ok im on it, this is what im doing....

.01= 1p
.02= 2p
.03= 3p
.04 = 4p
.05 = 1n
.06= 1n +1p
.08=1n +3p
.09=5n+4p
.1=1d
.11=1d+1p
.12=1d+2p

etc.......

its going to take a little while im on .31 now and i dont really see any patterns emerging that could potentially speed this up

stay tuned!

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07-10-2017 , 10:50 PM

PLBlow

grinder

Join Date: Sep 2011 Posts: 445

wait thats not true, theres a pattern with the pennies.

hang in there

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07-10-2017 , 11:11 PM

PLBlow

grinder

Join Date: Sep 2011 Posts: 445

interesting here is what i got....

there are 200 total penny combos as the penny patter repeats every unit of 5 cents as1+2+3+4+0+1+2+3+4+0. this is times 10 for each .01,.1,.2,.3 etc

then you can take each combo below and multiply it by 5, since it occurs 5 times withthe pennies

and

.05 = 1n
.1=1d
.15=1d+1n
.20=2d
.25=1q
.30=1q+1n
.35=1q+1d
.4=1q+1d+1n
.45=1q+2d
.50=2q
.55=2q+1n
.60=2q+1d
.65+2q+1d+1n
.70=2q+2d
.75=3q
.80=3q+1n
.85=3q+1d
.90=3q+1d+1n
.95=3q+2d

in the end we get

Pennies = 200/470 = 42.6%
Nickels = 40/470 = 8.5%
Dimes = 80/470 = 17%
Quarters = 150/470 = 31.9%

?????????

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07-11-2017 , 12:11 AM

NewOldGuy

Pooh-Bah

Join Date: Mar 2009 Posts: 5,935

The method you are using assumes all purchases are made without ever using coins.

Sent from my SM-G900V using Tapatalk

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07-11-2017 , 01:06 AM

PLBlow

grinder

Join Date: Sep 2011 Posts: 445

Quote:

Originally Posted by NewOldGuy

The method you are using assumes all purchases are made without ever using coins.

Sent from my SM-G900V using Tapatalk

yes this is true. it also assumes im never using exact change for a purchase

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07-11-2017 , 10:33 AM

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

Quote:

Assume that your change for purchases is evenly distributed form .01 to .99 (true?)

In reality we know prices ending in .99, .75, .50 and .25 are more common than say, .57

And it also depends which state you live in, because different sales taxes will lead to different common change amounts.

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07-11-2017 , 01:07 PM

#10

PLBlow

grinder

Join Date: Sep 2011 Posts: 445

yah thats true. does anyone know if i can take spare change to a bank? i dont want to roll it myself, and i dont want to use coinstar bc of the fees

it will be interesting to see how close the frequencies match the theoretical values

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07-11-2017 , 07:10 PM

#11

RustyBrooks

Carpal \'Tunnel

Join Date: Feb 2006 Posts: 24,647

Quote:

Originally Posted by PLBlow

Some banks yes, some no, some will do it for free only for customers, some won't do it for free for anyone. I have heard people have better luck at credit unions.

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07-12-2017 , 06:05 PM

#12

STinLA

old hand

Join Date: May 2009 Posts: 1,882

Quote:

Originally Posted by PLBlow

i dont want to use coinstar bc of the fees

If you use the option to load your payment on an Amazon gift card, there's no fee.

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12-08-2017 , 10:07 PM

#13

PLBlow

grinder

Join Date: Sep 2011 Posts: 445

Hey guys the results are in! I had $257.51 in change, which was comprised of 2513 coins.
The actual distribution I got is listed below, and I entered in the theoretical values we calculated to the right of those..

Pennies (735/2513) = 29.3% (42.6%)
Nickels (315/2513) = 12.5% (8.5%)
Dimes (482/2513) = 19.2% (17%)
Quarters (735/2513)= 29.3% (31.9%)

Pretty close!

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12-09-2017 , 08:44 AM

#14

akkopower1

centurion

Join Date: Feb 2017 Posts: 198

Quote:

Originally Posted by PLBlow

Looks good, not too surprising 1c and 5c are less than theoretical, 0.01, 0.02...ect would be less frequent.

If you take the experimental counts above as perfect; what would be the true distribution of prices?

It looks like two seperate problems to me, 1c and 5c are used to give correct change due to prices at the Cent level. Dimes and quarters are used to give change due to 10c price levels. Apart frim the times you need a nickel to get to the correct 10c level.

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