odds of your bill at the supermarket ending in an even dollar amount....

Doug · Feb 6, 2013

So I'm at Shoprite earlier today buying some groceries, my bill comes to $138 exactly, and the cashier comments on that.

I say well it's a one in a hundred shot, must happen about everyday !

There's and older white guy behind me in line, like 65-70, he chimes in and says it is more than a 100-1 probability for the order to end in .00.

So I point out it must end between .00 and .99 ( 100 outcomes) 99-1 if you do it that way way.

Assume a lot of different items in a random order with some weighed produce, this is as random as you can get.

I axe the guy to tell me why .00 is less likely than .07, .13, ,.69 or any other number. The best he could come up with was that the more items you buy the less likely the total is to end .00.

This is why casinos make money.

hno:

Murphy8276 · Feb 6, 2013

lol doug I think the guy was generalizing 1 out of 100 seemed like not as far out odds. I doubt he really thought bout ti much as u had till u asked puff_>>

-murph

terps1313 · Feb 6, 2013

Murphy8276 said:
lol doug I think the guy was generalizing 1 out of 100 seemed like not as far out odds. I doubt he really thought bout ti much as u had till u asked puff_>>

-murph

thats the problem... most people dont think about it or are too dumb to use common sense

Doug · Feb 6, 2013

I think even a real dummy should recognize that there is a 1% chance of each number coming up on a sufficiently random grocery order.

I explained why to him very civilly and asked why not ?

he just didn't get that there were 100 possibilities of equal probability.

ERockMoney · Feb 6, 2013

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This creates a situation where you are dealing with different probabilities with certain price points being used far more frequently and skewing the entire distribution of outcomes, similar to saying each block in a SB block pool has 1% chance of hitting, which is inaccurate due to the common scoring plays of three and seven.

Doug · Feb 6, 2013

ERockMoney said:
 I don’t believe this is accurate. To have a 1-100 chance of having your bill land on $X.00 there would need to be an even distribution used within the cent prices for products. Many products fall under the same cents pricing, i.e., $X.99 or $0.49 while prices ending in $X.00, $X.30, $X.50 are extremely uncommon. I don’t know the actual probabilities per number, but I think you get my point.

This creates a situation where you are dealing with different probabilities with certain price points being used far more frequently and skewing the entire distribution of outcomes, similar to saying each block in a SB block pool has 1% chance of hitting, which is inaccurate due to the common scoring plays of three and seven.

well you would tend to have stuff ending in .99....but I did say a large order with odd weight stuff like produce/ meat etc. included. there would also be a mix of taxable and non-taxable items involved.

Sure a lot of stuff ends in a 9, or is 10 for $10.

the random factor surely enters with a larger order and who knows what the bananas, pears, etc. weigh in at, the taxable stuff vs. non-taxable randomizes further.

Let me walk you around the store and select 100 items, you can see the prices, but have to guess the price of my weighed grapes, and other produce, plus taxes, bottle deposits, etc.

the last two digits of that bill will be pretty random.

shdw01 · Feb 6, 2013

because of the nature with things ending in .00 or .99 or .97, i think (as you guys have mentioned) that the more items purchased the more towards 1% the last two digits become.

but the nature of a cashier is there will always be a lot of people that buy 1-5 items....i bet those who buy under 15 items is 80%+ of the transactions.

ballpark figures mean that out of the remaining 20%, they have a 1% shot....so my ghetto math puts the odds at 1 in 500

TomGshotput · Feb 6, 2013

shdw01 said:
so my ghetto math puts the odds at 1 in 500

Ghetto is a very good description. You really believe if someone buys less than 15 items, the chance of it costing $x.00 is zero?

We all agree prices are not random. But that actually improves the chances. Items that are exactly $1 or $2 are more common than items that are $1.82 or $2.17

When someone buys two items and the total bill is $2, niether the cashier nor the customer will find it interesting enough to comment on.

YourAllAmerican · Feb 7, 2013

This is an interesting question. Get her on the case:
http://marilynvossavant.com/

shdw01 · Feb 7, 2013

TomGshotput said:
Ghetto is a very good description. You really believe if someone buys less than 15 items, the chance of it costing $x.00 is zero?

We all agree prices are not random. But that actually improves the chances. Items that are exactly $1 or $2 are more common than items that are $1.82 or $2.17

When someone buys two items and the total bill is $2, niether the cashier nor the customer will find it interesting enough to comment on.

i don't think zero but i think the odds are close enough to zero where it is negligible.

$1 and $2 are more common but i was considering a sales tax or excise tax.....if OP was in a state without sales tax, i highly doubt this would even be a discussion

Stylez · Feb 7, 2013

going to happen here a lot more now , if paying with cash since the penny is now gone they will be rounding total sale price. So no more 1,2,3,4,6,7,8,9. If paying with debit/credit price stays the same.

TomGshotput · Feb 7, 2013

shdw01 said:
i don't think zero but i think the odds are close enough to zero where it is negligible.

Way off. Only 12 states have sales tax on groceries. I used to buy a 75-cent newspaper and $1.25 two-Liter Diet Mtn Dew most mornings

But like Doug was saying, include produce and it just becomes much closer to totally random. So there are four items, three of them ending in .99, what are the chances the bag of apples ends in $x.03?

YourAllAmerican · Feb 7, 2013

If anyone has their receipt for a full trip to the grocery store, or a link to any list of store prices, I'll look into running a simulation and see just the results are.

BAGIANT · Feb 7, 2013

YourAllAmerican said:
This is an interesting question. Get her on the case:
http://marilynvossavant.com/

I love to read her column every week in Parade.

shdw01 · Feb 7, 2013

TomGshotput said:
Way off. Only 12 states have sales tax on groceries. I used to buy a 75-cent newspaper and $1.25 two-Liter Diet Mtn Dew most mornings

But like Doug was saying, include produce and it just becomes much closer to totally random. So there are four items, three of them ending in .99, what are the chances the bag of apples ends in $x.03?

Good point with produce.

In hawaii we have an excise tax....

YourAllAmerican · Feb 7, 2013

This had me curious, so I did decide to run a simulation. I loaded up a price list found online (here: http://www.aldispot.com/2011/02/grocery-price-comparison-list-aldi.html), began a loop to randomly select 30 items, then ran 1 million loops. Based on this rough simulation it looks like the chances of ending with a total of zero cents is pretty close to 1 in 100, but slightly less. Still, it cents amount doesn't look to be random, as some numbers come up more frequently and some almost not at all. With the way marketers like to end prices with a 9 ($1.99, $2.49, etc.) this makes sense.

One thing this simulation doesn't take into account is buying odd amounts of weight-based items. If oranges are $1.49 per pound, for example, this simulation just used the pricing of $1.49.

Here's how it worked out:

Cents Frequency Pct
12 20905 2.09%
43 20712 2.07%
62 20693 2.07%
37 20596 2.06%
93 20513 2.05%
23 20498 2.05%
87 20414 2.04%
68 20394 2.04%
18 20290 2.03%
73 20272 2.03%
98 20006 2.00%
6 19880 1.99%
26 19782 1.98%
48 19769 1.98%
56 19668 1.97%
31 19569 1.96%
81 19566 1.96%
76 19468 1.95%
1 19443 1.94%
51 19312 1.93%
59 19037 1.90%
29 19011 1.90%
4 18968 1.90%
79 18913 1.89%
34 18909 1.89%
54 18889 1.89%
9 18883 1.89%
84 18842 1.88%
15 18549 1.85%
95 18509 1.85%
65 18415 1.84%
40 18387 1.84%
45 18382 1.84%
90 18291 1.83%
20 18212 1.82%
70 18176 1.82%
82 11397 1.14%
53 11315 1.13%
32 11271 1.13%
3 11204 1.12%
78 11120 1.11%
57 11070 1.11%
28 10999 1.10%
42 10929 1.09%
46 10923 1.09%
96 10897 1.09%
17 10837 1.08%
67 10809 1.08%
7 10805 1.08%
92 10776 1.08%
71 10629 1.06%
21 10598 1.06%
89 10478 1.05%
14 10341 1.03%
64 10246 1.02%
39 10200 1.02%
35 9921 0.99%
85 9860 0.99%
60 9785 0.98%
10 9703 0.97%
25 9498 0.95%
75 9493 0.95%
50 9492 0.95%
0 9220 0.92%
88 379 0.04%
99 362 0.04%
97 360 0.04%
72 356 0.04%
63 332 0.03%
86 327 0.03%
22 320 0.03%
77 320 0.03%
74 317 0.03%
49 310 0.03%
52 293 0.03%
47 288 0.03%
36 282 0.03%
27 279 0.03%
24 272 0.03%
38 272 0.03%
13 268 0.03%
61 268 0.03%
11 230 0.02%
2 226 0.02%

5teamparlay · Feb 8, 2013

how about the odds at dollar tree where everything is a dollar...

now thats a different animal...

Doug · Feb 9, 2013

that all depends on sales taxes, pretty tough to come out even in a tax state.

trytrytry · Feb 9, 2013

you can say what you want but that 0.33 comes up lots more than 99-1

TomGshotput · Feb 9, 2013

YourAllAmerican said:
began a loop to randomly select 30 items,

Why did you decide to use the same number of items each time. If you did one million simulations, each with a random number of random items, wouldn't the results have been a lot different?