Author Topic: Episode #709  (Read 4082 times)

0 Members and 1 Guest are viewing this topic.

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #15 on: February 10, 2019, 05:05:40 PM »
My mother, when she was a young woman (this would be circa 1945) won the smallest prize in the Irish Sweepstakes. IIRC it was around $50, which in today’s money would be worth around $680. She decided that having won once, she was unlikely to win again and never gambled or bought another lottery ticket for the rest of her life.

Her reasoning was right for the wrong reason. Her chances of winning a second time were the same as her chances of winning the first time. But that chance was vanishingly small.

The lottery has been described as a tax on stupidity.

I used to play Lotto decades ago, until I picked two numbers and the supplementary number (which doesn’t win anything), and I decided that it was just a waste of money, and as you note ‘a tax on stupidity.’  Many people justify throwing their money away by noting that some of the proceeds go to charity.  Personally, I prefer to donate directly.

Lotto is heavily advertised.  Particularly when there’s a multimillion jackpot (which usually gets divided many times to the winners).  I’m never tempted to take part.  Even if I won $1 million, it wouldn’t change my life.

I remembered to buy the celery yesterday.  I used 675 g which produced 400 g of celery juice which I haven’t tried yet.  There’s therefore around 275 g of celery pulp, which I’m also going to try as part of my vegetable casserole.
Gebt ihr ihr ihr Buch zurück?

Offline The Latinist

  • Cyber Greasemonkey
  • Technical Administrator
  • Too Much Spare Time
  • *****
  • Posts: 7775
Re: Episode #709
« Reply #16 on: February 10, 2019, 05:39:05 PM »
So after all the hand-waving about why the letter-writer was wrong about probability calculations, they never did answer her direct question, which was, “What is the formula?”

If I'm remembering my statistics correctly, it's:

 

In other words, it's

1 - 365/365 * 364/365 * 363/365 * ... * (365-n)/365
« Last Edit: February 10, 2019, 05:45:50 PM by The Latinist »
I would like to propose...that...it is undesirable to believe in a proposition when there is no ground whatever for supposing it true. — Bertrand Russell

Offline Friendly Angel

  • Stopped Going Outside
  • *******
  • Posts: 4446
  • Post count reset to zero in both forum apocalypses
Re: Episode #709
« Reply #17 on: February 10, 2019, 06:40:41 PM »
I liked the new twist on the trolley problem:

If I were a doctor who had 50 patients with a fatal disease, and a treatment will kill one and cure 49... I'd give them all 50 the treatment of course.

But if I had to choose which ONE died, I wouldn't give it to any of them.
Amend and resubmit.

Offline daniel1948

  • Isn’t a
  • Reef Tank Owner
  • *********
  • Posts: 8609
  • I'd rather be paddling
Re: Episode #709
« Reply #18 on: February 10, 2019, 06:42:06 PM »
So after all the hand-waving about why the letter-writer was wrong about probability calculations, they never did answer her direct question, which was, “What is the formula?”

If I'm remembering my statistics correctly, it's:

 

In other words, it's

1 - 365/365 * 364/365 * 363/365 * ... * (365-n)/365

I figured it would be something along those lines, which would have taken about half a minute for them to say on the show. Hey, if they’re going to read a letter that asks for a formula, they should state the formula. They didn’t even give a particularly good general description.

But it’s not often that in my opinion they fail so badly at a segment.
Daniel
----------------
"Anyone who has ever looked into the glazed eyes of a soldier dying on the battlefield will think long and hard before starting a war."
-- Otto von Bismarck

Offline daniel1948

  • Isn’t a
  • Reef Tank Owner
  • *********
  • Posts: 8609
  • I'd rather be paddling
Re: Episode #709
« Reply #19 on: February 10, 2019, 06:45:37 PM »
I liked the new twist on the trolley problem:

If I were a doctor who had 50 patients with a fatal disease, and a treatment will kill one and cure 49... I'd give them all 50 the treatment of course.

But if I had to choose which ONE died, I wouldn't give it to any of them.

Even though that would result in all 50 dying?
Daniel
----------------
"Anyone who has ever looked into the glazed eyes of a soldier dying on the battlefield will think long and hard before starting a war."
-- Otto von Bismarck

Offline Friendly Angel

  • Stopped Going Outside
  • *******
  • Posts: 4446
  • Post count reset to zero in both forum apocalypses
Re: Episode #709
« Reply #20 on: February 10, 2019, 07:14:10 PM »
I liked the new twist on the trolley problem:

If I were a doctor who had 50 patients with a fatal disease, and a treatment will kill one and cure 49... I'd give them all 50 the treatment of course.

But if I had to choose which ONE died, I wouldn't give it to any of them.

Even though that would result in all 50 dying?

Of course.  And neither would you actively kill an innocent person to save 49. 
Amend and resubmit.

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #21 on: February 10, 2019, 07:18:47 PM »
So after all the hand-waving about why the letter-writer was wrong about probability calculations, they never did answer her direct question, which was, “What is the formula?”

If I'm remembering my statistics correctly, it's:

 

In other words, it's

1 - 365/365 * 364/365 * 363/365 * ... * (365-n)/365

I figured it would be something along those lines, which would have taken about half a minute for them to say on the show. Hey, if they’re going to read a letter that asks for a formula, they should state the formula. They didn’t even give a particularly good general description.

But it’s not often that in my opinion they fail so badly at a segment.

It would have taken considerably longer than half a minute to explain.  It’s just the formula of my explanation, which would take a few minutes to explain. 

I thought the later suggested method of calculation to be neater - with 23 people there’s 23 x 22/2 pairs of people ie 253 pairs. 

Why 23 x 22/2?  With the first person, there’s 22 pairs possible, with the 2nd person there’s 21 pairs, not already considered, possible, right down to the second last person for whom there’s only one possible pair not already mentioned, meaning there’s 22 + 21 + 20 + ...  + 1 pairs, or rearranging the numbers (22 + 1) + (21 + 2) + (20 + 3) + ... + (12 + 11).  In other ‘words’ 23 x 11 or 23 x 22/2. 

There’s a 364/365 chance one pair won’t share a birthday, so the chance of none of the pairs sharing a birthday is (364/365)253, which equals 0.49952284596342 (roughly).  So the chance of at least one of the pairs sharing a birthday (there could be more) is 0.50047715403658 (again roughly).

Neat isn’t it?  I love numbers.  It must appeal to my inner Asperger’s.
« Last Edit: February 10, 2019, 07:39:12 PM by bachfiend »
Gebt ihr ihr ihr Buch zurück?

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #22 on: February 10, 2019, 08:42:17 PM »
Well, I made a batch of celery juice this morning.  I used 675 g of celery which yielded 400 g of celery juice.

It tastes like celery surprising enough.

Looking at a database, 400 ml of celery juice (which is rather a lot) contains 34 Calories.  It seems as though a lot of the Calories must have been left in the pulp since 675 g of celery contains 108 Calories.  As well as most of the 11 g of fibre (there’s still 3 g in the juice apparently).  Little fat.  Little protein.

Looking at the micronutrients, no numbers really jump out as being particularly significant, with % of RDA usually not exceeding 10%.  Vitamin K (which your gut bacteria makes for you) gets to 50%.  And folate gets to 19%.

So celery is really just a green coloured celery flavoured drink containing a little folic acid, which may be of slight benefit if you’re pregnant.

I don’t know if I want to continue with making it.  At my supermarket, 675 g of celery cost $3.50, which makes celery juice rather expensive at around $8.75 a litre.  I buy carrots at 90 cents a kilogram, which would make around 500 g of carrot juice, or around $2 a litre.  And I love carrot juice.  Perhaps a little too much.  I wonder if my palms are starting to go a tiny bit orange?  But anyway - hypercarotenaemia is biologically benign.
Gebt ihr ihr ihr Buch zurück?

Offline brilligtove

  • Too Much Spare Time
  • ********
  • Posts: 7414
  • Ignorance can be cured. Stupidity, you deal with.
Re: Episode #709
« Reply #23 on: February 10, 2019, 10:19:39 PM »
...most of the doctors I know would not hesitate to make that decision.
evidence trumps experience | performance over perfection | responsibility – authority = scapegoat | emotions motivate; data doesn't

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #24 on: February 10, 2019, 10:46:08 PM »
...most of the doctors I know would not hesitate to make that decision.

It’s the trolley problem.  Would you divert a runaway trolley onto a sidetrack killing one worker so as to not allow five workers on the main track to be killed?  Would you push a very large and fat person on a bridge to derail the trolley, almost certainly killing one person to save five?  Most people answer ‘yes, no’ respectively.  It’s very, very artificial, but I would have answered ‘no’ to both.  The five workers should have been looking out and taken care of themselves!

I can’t quite work out how the trolley problem could be reworked to the medical setting.  Perhaps you’ve got some miracle medical procedure which would cure 49 people with an otherwise fatal illness, but it involves sacrificing one person, whom you get to choose, in order to harvest all his (or her) tissue in order to prepare a remedy to be given to the others?

If that were possible, I’m pretty certain that all doctors would give the same answers.  It’s OK to treat 50 people knowing that one person will die (and you don’t know whom) with 49 being saved from a certain death, but it’s not OK to choose one person to kill knowing that you’re going to save 49, the same number of people.
Gebt ihr ihr ihr Buch zurück?

Offline Soldier of FORTRAN

  • Reef Tank Owner
  • *********
  • Posts: 9628
  • Cache rules everything around me.
Re: Episode #709
« Reply #25 on: February 10, 2019, 11:01:33 PM »
It’s the trolley problem.  Would you divert a runaway trolley onto a sidetrack killing one worker so as to not allow five workers on the main track to be killed?  Would you push a very large and fat person on a bridge to derail the trolley, almost certainly killing one person to save five?  Most people answer ‘yes, no’ respectively.  It’s very, very artificial, but I would have answered ‘no’ to both.  The five workers should have been looking out and taken care of themselves!

I would say yes/no.

On the trolley and tracks? Steering is my responsibility.  The tracks are my area of operation.*

On the overpass, I'm just a bystander.


* You're driving a truck. The brakes go out and there is a farmer's market ahead.  You have seconds to impact. Do you aim where the crowd is thinnest?
« Last Edit: February 10, 2019, 11:03:45 PM by Soldier of FORTRAN »
If global warming is real then how come I just felt this chill down my spine?

Offline DevoutCatalyst

  • Well Established
  • *****
  • Posts: 1549
Re: Episode #709
« Reply #26 on: February 10, 2019, 11:02:43 PM »
The trolley would run over the fat man and continue on and kill the others, too. Congratulations, hero. 

Offline Soldier of FORTRAN

  • Reef Tank Owner
  • *********
  • Posts: 9628
  • Cache rules everything around me.
Re: Episode #709
« Reply #27 on: February 10, 2019, 11:04:10 PM »
The trolley would run over the fat man and continue on and kill the others, too. Congratulations, hero.

Fights climate change.
If global warming is real then how come I just felt this chill down my spine?

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #28 on: February 10, 2019, 11:23:39 PM »
It’s the trolley problem.  Would you divert a runaway trolley onto a sidetrack killing one worker so as to not allow five workers on the main track to be killed?  Would you push a very large and fat person on a bridge to derail the trolley, almost certainly killing one person to save five?  Most people answer ‘yes, no’ respectively.  It’s very, very artificial, but I would have answered ‘no’ to both.  The five workers should have been looking out and taken care of themselves!

I would say yes/no.

On the trolley and tracks? Steering is my responsibility.  The tracks are my area of operation.  (You're driving a truck. The brakes go out and there is a farmer's market ahead.  You have seconds to impact.

 Do you aim where the crowd is thinnest?)

On the overpass, I'm just a bystander.

Most people would agree with you.  If I had only seconds to decide what to do driving a truck (which is certainly not ever going to happen), I’m certain I that I would freeze and not make a decision.  Perhaps if you could choose between aiming at where the crowd is densest (but with a chance of hitting no one), or aiming at where the crowd is thinnest, but you’re certain to hit someone?  Perhaps at both sides of the crowd, there are many more people, but few in the centre?  You can either not change your direction and hit the crowd centrally, and certainly kill a few, or attempt to steer away, and hit no one, but possibly, even probably, kill many? 

It’s the ‘Titanic’ scenario.  If the officer in charge hadn’t attempted to steer away from the iceberg, then the ship wouldn’t have been sunk.  There have been ships that have run into icebergs headon and survived, albeit badly dented.  And on the Titanic some people might be killed if they happened to be descending stairs when the ship came to an abrupt halt, instead of the actual 1500+ death toll.

I don’t know how I’d answer.  I think most people would probably answer that they’d try to miss the crowd and the iceberg.
Gebt ihr ihr ihr Buch zurück?

Offline fuzzyMarmot

  • Seasoned Contributor
  • ****
  • Posts: 673
Re: Episode #709
« Reply #29 on: February 11, 2019, 12:18:01 AM »
So after all the hand-waving about why the letter-writer was wrong about probability calculations, they never did answer her direct question, which was, “What is the formula?”

If I'm remembering my statistics correctly, it's:

 

In other words, it's

1 - 365/365 * 364/365 * 363/365 * ... * (365-n)/365

I figured it would be something along those lines, which would have taken about half a minute for them to say on the show. Hey, if they’re going to read a letter that asks for a formula, they should state the formula. They didn’t even give a particularly good general description.

But it’s not often that in my opinion they fail so badly at a segment.

It would have taken considerably longer than half a minute to explain.  It’s just the formula of my explanation, which would take a few minutes to explain. 

I thought the later suggested method of calculation to be neater - with 23 people there’s 23 x 22/2 pairs of people ie 253 pairs. 

Why 23 x 22/2?  With the first person, there’s 22 pairs possible, with the 2nd person there’s 21 pairs, not already considered, possible, right down to the second last person for whom there’s only one possible pair not already mentioned, meaning there’s 22 + 21 + 20 + ...  + 1 pairs, or rearranging the numbers (22 + 1) + (21 + 2) + (20 + 3) + ... + (12 + 11).  In other ‘words’ 23 x 11 or 23 x 22/2. 

There’s a 364/365 chance one pair won’t share a birthday, so the chance of none of the pairs sharing a birthday is (364/365)253, which equals 0.49952284596342 (roughly).  So the chance of at least one of the pairs sharing a birthday (there could be more) is 0.50047715403658 (again roughly).

Neat isn’t it?  I love numbers.  It must appeal to my inner Asperger’s.

I think your explanation has an error. You can't simply multiply probabilities unless they are independent events (and in this case, the events of different pairs not sharing birthdays are not independent). You should note that your expression for the solution does not match the formula quoted above. It is a very, very close approximation, though. I've posted a graph here: https://www.scribd.com/document/399355955/Birthday
I am not smart enough to figure out how to embed the pdf  :D
« Last Edit: February 11, 2019, 12:23:06 AM by fuzzyMarmot »