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*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*

Copy that, Command. Sidearm is loaded and ready to neutralize hostile soft drinks. Going comms dark during infiltration and initial recon.

PFC drainbamage, over and out.

Krrrssch

View attachment 1457131082242.jpg
 
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?

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.


 
I got HBC 429, Sorachi Ace, Citra, and Amarillo on hand. Next beer needs to be with some combo of those. Anybody got any recommends? Don't even know what hbc 429 is supposed to be like, it and sorachi ace (which i've been wanting to try) were at this grab basket at the second biggest Norwegian national competition (but that one the public votes on their favorite).
 
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.







Oooooh. Maybe we should throw a wildcard in the 50K game and double down if it happens to be the winners birthday?
 
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.



.

View attachment 1457132132118.jpg
 
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.



Thank you for Googlethinking for me. Obviously I didn't expect a significant difference, but clearly there's a marginally insignificant difference.

My mind is too flustered with both stress for my upcoming exam next weekend, and stress for tomorrow morning's possibly most important football match of my lifetime. I will be in the pub drinking at 7:45 am with the local Yiddos, undoubtedly next to a sea of red, and hopefully by then end our boots soaked in their tears. COYS!
 
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.



I have nothing cool to add to this, I just wanted to add to the clutter of those watching at home. Happy scrolling, ********!
 
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...
 
Oh yea. Lagunitas IPA.

IMG_20160304_171841.jpg
 
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...

The first one I brewed, I think largely based off of @Qhrumphf 's, is still my favorite iteration.

Did:
70% MO
14% C60
9% Pale Chocolate
7% Biscuit

Fuggles and Wyeast 1318.

1.035 OG, 1.010 FG, 18 IBU or so.

Reaper's looks good but I think you'll be appreciative of what the biscuit malt brings to the table. Ive still never had a commercial DEM so can't say how accurate it is but damn it's tasty.
 
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