WesleyS
Well-Known Member
- Joined
- May 1, 2012
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Admiring my free schwag haul
View attachment ImageUploadedByHome Brew1457130816.410878.jpg
View attachment ImageUploadedByHome Brew1457130816.410878.jpg
*krcrssch* Overwatch to PFC drainbamage, come in, over. *krrssch*
*krssch* New intel suggests a flask in the loadout for this mission, do you copy? High risk of failure at next waypoint. Mission critical, Foxtrot, Lima, Alpha, Sierra, Kilo necessary for success. Do you copy? Over. *krrscch*
Tasting some beers at Olde Hickory.
View attachment 341734
Yes, but that's not including that leap year happens only once every 4 years, but rather assuming 366 days every year, or is it?
What's everyone's birthday here? We have like 40 friendly regulars, surely some of us have friendly birthdays because maths?
July 5th.
You are correct. Google says this:
BUT WHAT ABOUT LEAP YEAR?
The original problem can be solved with a slide rule, which is exactly what I did when I first heard it many, many years ago.
If we add February 29 to the mix, it gets considerably more complicated. In this case, we make some additional assumptions:
Equal numbers of people are born on days other than February 29.
The number of people born on February 29 is one-fourth of the number of people born on any other day.
Hence the probability that a randomly selected person was born on February 29 is 0.25/365.25, and the probability that a randomly selected person was born on another specified day is 1/365.25.
The probability that N persons, possibly including one born on February 29, have distinct birthdays is the sum of two probabilities:
That the N persons were born on N different days other than February 29.
That the N persons were born on N different days, and include one person born on February 29.
The probabilities add because the two cases are mutually exclusive.
Now each probability can be expressed recursively:
double different_birthdays_excluding_Feb_29(int n)
{
return n == 1 ? 365.0/365.25 :
different_birthdays_excluding_Feb_29(n-1) * (365.0-(n-1)) / 365.25;
}
double different_birthdays_including_Feb_29(int n)
{
return n == 1 ? 0.25 / 365.25 :
different_birthdays_including_Feb_29(n-1) * (365.0-(n-2)) / 365.25 +
different_birthdays_excluding_Feb_29(n-1) * 0.25 / 365.25;
}
A program to display the probabilities goes something like this:
void main(void)
{
int n;
for (n = 1; n <= 366; n++)
printf("%3d: %e\n", n, 1.0-different_birthdays_excluding_Feb_29(n) -
different_birthdays_including_Feb_29(n));
}
The result is something like this:
1: -8.348357e-18
2: 2.736445e-03
3: 8.194354e-03
4: 1.633640e-02
5: 2.710333e-02
***
20: 4.110536e-01
21: 4.432853e-01
22: 4.752764e-01
23: 5.068650e-01
24: 5.379013e-01
25: 5.682487e-01
***
As expected, the probabilities are slightly lower, because there is a lower probability of matching birthdays when there are more possible birthdays. But the smallest number with probability greater than 0.5 is still 23.
Of course, a mathematical purist may argue that leap years don't always come every four years, so the calculations need further modification. However, the last quadrennial year that wasn't a leap year was 1900, and the next one will be 2100. The number of persons now living who were born in 1900 is so small that I think our approximation is valid for all practical purposes. But you are welcome to make the required modifications if you wish.
Just went in for 1....
You are correct. Google says this:
BUT WHAT ABOUT LEAP YEAR?
The original problem can be solved with a slide rule, which is exactly what I did when I first heard it many, many years ago.
If we add February 29 to the mix, it gets considerably more complicated. In this case, we make some additional assumptions:
Equal numbers of people are born on days other than February 29.
The number of people born on February 29 is one-fourth of the number of people born on any other day.
Hence the probability that a randomly selected person was born on February 29 is 0.25/365.25, and the probability that a randomly selected person was born on another specified day is 1/365.25.
The probability that N persons, possibly including one born on February 29, have distinct birthdays is the sum of two probabilities:
That the N persons were born on N different days other than February 29.
That the N persons were born on N different days, and include one person born on February 29.
The probabilities add because the two cases are mutually exclusive.
Now each probability can be expressed recursively:
double different_birthdays_excluding_Feb_29(int n)
{
return n == 1 ? 365.0/365.25 :
different_birthdays_excluding_Feb_29(n-1) * (365.0-(n-1)) / 365.25;
}
double different_birthdays_including_Feb_29(int n)
{
return n == 1 ? 0.25 / 365.25 :
different_birthdays_including_Feb_29(n-1) * (365.0-(n-2)) / 365.25 +
different_birthdays_excluding_Feb_29(n-1) * 0.25 / 365.25;
}
A program to display the probabilities goes something like this:
void main(void)
{
int n;
for (n = 1; n <= 366; n++)
printf("%3d: %e\n", n, 1.0-different_birthdays_excluding_Feb_29(n) -
different_birthdays_including_Feb_29(n));
}
The result is something like this:
1: -8.348357e-18
2: 2.736445e-03
3: 8.194354e-03
4: 1.633640e-02
5: 2.710333e-02
***
20: 4.110536e-01
21: 4.432853e-01
22: 4.752764e-01
23: 5.068650e-01
24: 5.379013e-01
25: 5.682487e-01
***
As expected, the probabilities are slightly lower, because there is a lower probability of matching birthdays when there are more possible birthdays. But the smallest number with probability greater than 0.5 is still 23.
Of course, a mathematical purist may argue that leap years don't always come every four years, so the calculations need further modification. However, the last quadrennial year that wasn't a leap year was 1900, and the next one will be 2100. The number of persons now living who were born in 1900 is so small that I think our approximation is valid for all practical purposes. But you are welcome to make the required modifications if you wish.
Because some other dummy had it locked up. I've only met two other people born on 7/7 but never on the same year
You are correct. Google says this:
BUT WHAT ABOUT LEAP YEAR?
The original problem can be solved with a slide rule, which is exactly what I did when I first heard it many, many years ago.
If we add February 29 to the mix, it gets considerably more complicated. In this case, we make some additional assumptions:
Equal numbers of people are born on days other than February 29.
The number of people born on February 29 is one-fourth of the number of people born on any other day.
Hence the probability that a randomly selected person was born on February 29 is 0.25/365.25, and the probability that a randomly selected person was born on another specified day is 1/365.25.
The probability that N persons, possibly including one born on February 29, have distinct birthdays is the sum of two probabilities:
That the N persons were born on N different days other than February 29.
That the N persons were born on N different days, and include one person born on February 29.
The probabilities add because the two cases are mutually exclusive.
Now each probability can be expressed recursively:
double different_birthdays_excluding_Feb_29(int n)
{
return n == 1 ? 365.0/365.25 :
different_birthdays_excluding_Feb_29(n-1) * (365.0-(n-1)) / 365.25;
}
double different_birthdays_including_Feb_29(int n)
{
return n == 1 ? 0.25 / 365.25 :
different_birthdays_including_Feb_29(n-1) * (365.0-(n-2)) / 365.25 +
different_birthdays_excluding_Feb_29(n-1) * 0.25 / 365.25;
}
A program to display the probabilities goes something like this:
void main(void)
{
int n;
for (n = 1; n <= 366; n++)
printf("%3d: %e\n", n, 1.0-different_birthdays_excluding_Feb_29(n) -
different_birthdays_including_Feb_29(n));
}
The result is something like this:
1: -8.348357e-18
2: 2.736445e-03
3: 8.194354e-03
4: 1.633640e-02
5: 2.710333e-02
***
20: 4.110536e-01
21: 4.432853e-01
22: 4.752764e-01
23: 5.068650e-01
24: 5.379013e-01
25: 5.682487e-01
***
As expected, the probabilities are slightly lower, because there is a lower probability of matching birthdays when there are more possible birthdays. But the smallest number with probability greater than 0.5 is still 23.
Of course, a mathematical purist may argue that leap years don't always come every four years, so the calculations need further modification. However, the last quadrennial year that wasn't a leap year was 1900, and the next one will be 2100. The number of persons now living who were born in 1900 is so small that I think our approximation is valid for all practical purposes. But you are welcome to make the required modifications if you wish.
You are correct. Google says this:
BUT WHAT ABOUT LEAP YEAR?
The original problem can be solved with a slide rule, which is exactly what I did when I first heard it many, many years ago.
If we add February 29 to the mix, it gets considerably more complicated. In this case, we make some additional assumptions:
Equal numbers of people are born on days other than February 29.
The number of people born on February 29 is one-fourth of the number of people born on any other day.
Hence the probability that a randomly selected person was born on February 29 is 0.25/365.25, and the probability that a randomly selected person was born on another specified day is 1/365.25.
The probability that N persons, possibly including one born on February 29, have distinct birthdays is the sum of two probabilities:
That the N persons were born on N different days other than February 29.
That the N persons were born on N different days, and include one person born on February 29.
The probabilities add because the two cases are mutually exclusive.
Now each probability can be expressed recursively:
double different_birthdays_excluding_Feb_29(int n)
{
return n == 1 ? 365.0/365.25 :
different_birthdays_excluding_Feb_29(n-1) * (365.0-(n-1)) / 365.25;
}
double different_birthdays_including_Feb_29(int n)
{
return n == 1 ? 0.25 / 365.25 :
different_birthdays_including_Feb_29(n-1) * (365.0-(n-2)) / 365.25 +
different_birthdays_excluding_Feb_29(n-1) * 0.25 / 365.25;
}
A program to display the probabilities goes something like this:
void main(void)
{
int n;
for (n = 1; n <= 366; n++)
printf("%3d: %e\n", n, 1.0-different_birthdays_excluding_Feb_29(n) -
different_birthdays_including_Feb_29(n));
}
The result is something like this:
1: -8.348357e-18
2: 2.736445e-03
3: 8.194354e-03
4: 1.633640e-02
5: 2.710333e-02
***
20: 4.110536e-01
21: 4.432853e-01
22: 4.752764e-01
23: 5.068650e-01
24: 5.379013e-01
25: 5.682487e-01
***
As expected, the probabilities are slightly lower, because there is a lower probability of matching birthdays when there are more possible birthdays. But the smallest number with probability greater than 0.5 is still 23.
Of course, a mathematical purist may argue that leap years don't always come every four years, so the calculations need further modification. However, the last quadrennial year that wasn't a leap year was 1900, and the next one will be 2100. The number of persons now living who were born in 1900 is so small that I think our approximation is valid for all practical purposes. But you are welcome to make the required modifications if you wish.
What's everyone's birthday here? We have like 40 friendly regulars, surely some of us have friendly birthdays because maths?
July 5th.
What's the consensus on DEM recipes?
I normally use Reaper's Mild, but would be interested in tinkering with it a bit more.
Kegerator is almost empty, which in and of itself is unacceptable. Need to get 10g of DEM going soon...
Now the chocolate RIS with my jägerschnitzel.
View attachment 341741
What's the consensus on DEM recipes?
I normally use Reaper's Mild, but would be interested in tinkering with it a bit more.
Kegerator is almost empty, which in and of itself is unacceptable. Need to get 10g of DEM going soon...