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Always find it interesting how people's brains work on this question. One way you might look at it would be as a question of timing - when are you making the prediction. E.g if you roll a 6 and then go "what are the chances of rolling another 6?", its 1 in 6. But if you make the prediction before you start and say "what are the chances of rolling 2 6s?", it's 1 in 36 because 2 separate things need to go your way, whereas in the first question the first roll has already gone your way. It's the compounding effect of doing things in sequence.

I always think it's helpful for understanding the commonly known "birthday paradox" as well - that in any group of 23 people its more likely than not that 2 of them will share a birthday. You think of it as starting off in a room with just yourself, then one by one people enter. What is the probability that you all have different birthdays? The first person to enter (besides you) has a 364/365 chance of having a different birthday to you. The second person has a 363/365 chance of having a birthday not shared by anyone else in the room, the third person has a 362/365 chance, and so on. Once you start multiplying those fractions together it doesn't take too long before the product becomes less than 1/2. It's easier to think of the series of 23 people entering the room one by one than it is to start out thinking of the 23 people in the room by the end.

 

Edited by ThatBoyRonaldo

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The thing I've never been able to get my head round is the one about the man who has two kids. If you know that one is a girl, what are the odds that the other is a boy? Apparently it's 2/3 because you can have the combinations Boy-Boy, Boy-Girl, Girl-Boy and Girl-Girl. Knowing that one is a girl eliminates the first possibility but the others remain. It changes if you specify that the older child is a girl which knocks out the second possibility too, but I can't figure out why this is so important.

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13 hours ago, Mr. Alli said:

Are 24hr Asda etc now shutting early again? 

Why do the doors on 24hr Asda have locks?

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15 hours ago, Zen Archer Esq. said:

 

Did August Darnell ever resolve his dispute with the CSA regarding Annie?

Did Dionne Warwick ever get to San Jose? 

And isn't it fortunate she wasn't going to Cockermouth? 

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13 hours ago, Alert Mongoose said:

If there are 50 numbers in a hat and you pick out the number 20 and then put it back in again are the odds that it would come out on the next pick the same as any other number?

What sort of hat?

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.... and what method is being used for the mixing?  Are we presuming that these numbers are on equally sized paper tickets, or are they sellotaped-together fridge magnet numbers, the size and shape of which will play a factor (9s and 6s are more likely to become entangled than 1s and 7s).  So many fundamental questions remain unanswered here.  

Eta: took me long enough to get my head around the Monty Hall problem.  Mathematical concepts and I aren't a particularly great mix I have to admit

Edited by Hedgecutter

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1 hour ago, ThatBoyRonaldo said:

 

Always find it interesting how people's brains work on this question. One way you might look at it would be as a question of timing - when are you making the prediction. E.g if you roll a 6 and then go "what are the chances of rolling another 6?", its 1 in 6. But if you make the prediction before you start and say "what are the chances of rolling 2 6s?", it's 1 in 36 because 2 separate things need to go your way, whereas in the first question the first roll has already gone your way. It's the compounding effect of doing things in sequence

 

Yeah, that’s where I was getting stuck. I was thinking at the point of picking out the second ball.

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13 minutes ago, Alert Mongoose said:

Yeah, that’s where I was getting stuck. I was thinking at the point of picking out the second ball.

That was my impression too.

I guess another example would be when folk say that the odds of 1, 2, 3, 4, 5 & 6 getting drawn out of the lottery machine are just as likely as any other combination*, but the odds of them being drawn out in that very specific order are significantly lower. 

*did this not happen fairly recently in Greece or some place like that?  Eta:  It was the South African lottery in which 5, 6, 7, 8, 9 & 10 came out in December... although the fact that 20 people got this, which was statistically mental for any draw, resulted in allegations of fraud over it.  Unthinkable in a place like South Africa.

Edited by Hedgecutter

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See if Windows is installing an update as part of shutting down the computer, how long should you wait before giving up and switching it off? Mine's been at it for over four hours now.

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On 06/01/2021 at 00:01, Alert Mongoose said:

If there are 50 numbers in a hat and you pick out the number 20 and then put it back in again are the odds that it would come out on the next pick the same as any other number?

Yes.

EDIT: Assuming the numbers are shuffled / jumbled up sufficiently for the pick to be random.

Edited by Gaz

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3 minutes ago, DiegoDiego said:

See if Windows is installing an update as part of shutting down the computer, how long should you wait before giving up and switching it off? Mine's been at it for over four hours now.

Only time I had anything more than half an hour was when they gave the free upgrade to Windows 10. Thinking about it 10 minutes max since.

Edited by welshbairn

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10 hours ago, Gaz said:

Yes.

EDIT: Assuming the numbers are shuffled / jumbled up sufficiently for the pick to be random.

Whoa...I thought I had it and now you're saying it's equally likely to come out twice in a row as not?

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That was my impression too.
I guess another example would be when folk say that the odds of 1, 2, 3, 4, 5 & 6 getting drawn out of the lottery machine are just as likely as any other combination*, but the odds of them being drawn out in that very specific order are significantly lower. 


720 times more unlikely

Although still the same as any other permutation being drawn out in any given exact order


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On 06/01/2021 at 13:26, tamthebam said:

Did Dionne Warwick ever get to San Jose? 

And isn't it fortunate she wasn't going to Cockermouth? 

OD9VXo9.jpg

Bell-End-Rowley-Regis-3179021.jpg

back_passage_183r6mf-183r6mu.jpg

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On 06/01/2021 at 13:44, Hedgecutter said:

That was my impression too.

I guess another example would be when folk say that the odds of 1, 2, 3, 4, 5 & 6 getting drawn out of the lottery machine are just as likely as any other combination*, but the odds of them being drawn out in that very specific order are significantly lower. 

*did this not happen fairly recently in Greece or some place like that?  Eta:  It was the South African lottery in which 5, 6, 7, 8, 9 & 10 came out in December... although the fact that 20 people got this, which was statistically mental for any draw, resulted in allegations of fraud over it.  Unthinkable in a place like South Africa.

Richard Feynman once started a lecture on probability with "Something incredible just happened to me on the way here, I was walking through the parking lot and passed a car with a plate that read "6GDG486". What are the chances of that?!?"

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How does right to roam apply to farm tracks, particularly the 'aggregate with the grassy stripe down the middle' type that leads past (but not through) a farmyard?

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Why do the doors on 24hr Asda have locks?
Otherwise they'd get raided on the days of the year they close.

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