KB1 tasked me with determining the odds of getting exactly one Liberty Quarter (“LQ”) and one Wheat Penny (“WP”) as the result of a cash transaction. The following analysis is necessarily built on a lot of assumptions, but I think it makes for a decent ballpark estimate. Here goes:
Getting exactly one quarter and one penny as change only happens when a transaction total comes to $X.74. We first need to calculate the odds of that happening. I assume half of all cash transactions in NYC end in an even-quarter increment (cab ride with tip is $12.00; Diet Coke at deli is $1.50). All other transactions are distributed evenly across the remaining 96 two-digit cent outcomes. Thus the probability of receiving exactly one quarter and one penny in a transaction is .5 x 1/96 = 0.52%.
Next, we need to identify the probability of that quarter being an LQ. Somebody on the interweb helpfully studied a sample of 1,000 quarters last year and noted the following: (1) there were no quarters before 1965, the year the mint stopped putting silver in quarters, (2) 41% were from this decade, (3) 28% were from the ‘90s, (4) 18% were from the ‘80s, (5) the remaining 13% were from 1965 – 1979, (6) across each bucket, the years were fairly evenly distributed. Thus the probability that a random quarter will be an LQ (at least in 2008) is 0.13/15 = 0.867%.
We now need to run the same analysis for pennies. I didn’t find anything useful on the web. Indeed, KB1’s stash of LQs and WPs would be hugely helpful here. In the absence of anything else, I know I receive many more LQs than WPs these days. Probably 4-1. So let’s say that the probability of a random penny being a WP is about a quarter of the probability that a quarter is a LQ, or 0.00867/4 = 0.217%.
The probability of KB1’s transaction is thus 0.52% x 0.867% x 0.217% = 0.00001%, or one out of every 10 million cash transactions.
Let’s say the average New Yorker makes 5 cash transactions per day. We would expect to see KB1’s change event happen once every 2 million person-days, or once every 5,600 person-years.
Of course, there are 8 million people in NYC. So we would expect KB1’s change event to happen to 4 people in the City every day. Not exactly winning the lottery, but not bad, either.
Getting exactly one quarter and one penny as change only happens when a transaction total comes to $X.74. We first need to calculate the odds of that happening. I assume half of all cash transactions in NYC end in an even-quarter increment (cab ride with tip is $12.00; Diet Coke at deli is $1.50). All other transactions are distributed evenly across the remaining 96 two-digit cent outcomes. Thus the probability of receiving exactly one quarter and one penny in a transaction is .5 x 1/96 = 0.52%.
Next, we need to identify the probability of that quarter being an LQ. Somebody on the interweb helpfully studied a sample of 1,000 quarters last year and noted the following: (1) there were no quarters before 1965, the year the mint stopped putting silver in quarters, (2) 41% were from this decade, (3) 28% were from the ‘90s, (4) 18% were from the ‘80s, (5) the remaining 13% were from 1965 – 1979, (6) across each bucket, the years were fairly evenly distributed. Thus the probability that a random quarter will be an LQ (at least in 2008) is 0.13/15 = 0.867%.
We now need to run the same analysis for pennies. I didn’t find anything useful on the web. Indeed, KB1’s stash of LQs and WPs would be hugely helpful here. In the absence of anything else, I know I receive many more LQs than WPs these days. Probably 4-1. So let’s say that the probability of a random penny being a WP is about a quarter of the probability that a quarter is a LQ, or 0.00867/4 = 0.217%.
The probability of KB1’s transaction is thus 0.52% x 0.867% x 0.217% = 0.00001%, or one out of every 10 million cash transactions.
Let’s say the average New Yorker makes 5 cash transactions per day. We would expect to see KB1’s change event happen once every 2 million person-days, or once every 5,600 person-years.
Of course, there are 8 million people in NYC. So we would expect KB1’s change event to happen to 4 people in the City every day. Not exactly winning the lottery, but not bad, either.
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