Expanding on the logic riddle:

[frigidweirdo]

I got in a heated argument with someone over a similar riddle involving tossing a coin. Say you flip a coin five times, and all five times it’s tails. He was convinced that meant the sixth time had a higher probability of being heads. No! It’s still 50/50!

Also, people won’t believe that if you play the lotto with the numbers: 1,2,3,4,5,6,7 it has just as much chance of winning as any other single combination of numbers.

it’s amazing how most people do not understand the basics of probability.

I'd disagree with the last one about the lotto numbers. It's only make a small difference but I think the chances are lower.

If you were to look at the statistics and see how often neighboring numbers come up next to each other, you might find that things are not necessarily equal.

UK Lotto Results: Full Draw History and Winning Numbers

Check latest UK Lotto results and full draw history (since 19 October 1994). Find past winning numbers and verify your tickets!

www.beatlottery.co.uk

Here's a lottery, I think it's the UK lottery, I'm not sure.

5th Jan they had two consecutive numbers
22nd December they had two consecutive numbers
11th December they had three consecutive numbers together
8th December they had two consecutive numbers together
4th December they had two consecutive
1st December they had one consecutive

Not bad, in the space of 40 days with 12 draws you had 4 pairs, 1 double pair and one triple. But nothing more than a triple.

What are the statistical chances of getting a double?

Well, 7 doubles in 12 draws. That's a high frequency. Chances of a triple? One in 12. Chances of a quadruple? Much less.

Lotto Statistics - Most Common Lotto Numbers

View the up to date Lotto statistics and comprehensive analysis, including number frequency graphs, most drawn numbers, jackpot history and much more.

www.national-lottery.com

Here's the frequency of the numbers. The lottery certainly isn't totally random. People get balls, they go through a process that might repeat, the machine goes through a process that repeats and perhaps there are reasons why certain numbers come out more often.

13 and 14 are the most common pair. Again, maybe this is just chance, maybe it's for some reason. Other lotteries might find it works differently. Triple numbers, 8,9,10 has appeared three times. Others have appeared twice.

Thunderball Statistics

Thunderball Statistics including the most common winning Thunderball numbers, a frequency table, the most-picked numbers and more.

www.lottery.co.uk

Bizarrely, this thunderball thing also has numbers in the teens quite high up too. Same company, I think.

Have consecutive numbers even been drawn in the lottery (like 1, 2, 3, 4, 5, 6)?

Answer (1 of 10): I don’t know if it happened but it can be interesting to calculate the probability: If the lottery has n possible numbers and you have to pick k numbers to make your ticket: There are n-k+1 possible consecutive sequences (for example a series of 4 numbers from 1 to 10 has to b...

www.quora.com

Apparently in 2016 1,2,3,4,20,21 was drawn, a quadruple.


It happens. What about five consecutive numbers?

It depends on how you approach the statistics really.

 

[Fort Fun Indiana]

Because, in and of itself, each individual card draw will always have a 50/50 chance, but the chance that *two* consecutive draws will be the same color lowers the probability. Am I right?

Yes, that is part of the larger solution.

 

[braalian]

Yes, that is part of the larger solution.

What else am I missing?

(genuinely curious)

 

[frigidweirdo]

No. I only shuffled the 2 cards I drew from the infinite deck. An infinite deck does not require shuffling.

Then the problem is with how you write this "them" means what? I took it to mean "all the cards", you meant it to mean two cards.

 

[Toddsterpatriot]

Correct. Intentional and necessary red herring (in scenarios 3 and 4), so as not to give clues to the correct answer.

Whatever reason it was put there, it made the odds 50/50.

 

[Toddsterpatriot]

What else am I missing?

(genuinely curious)

The odds are 50/50, in all his scenarios.

 

[Fort Fun Indiana]

I'd disagree with the last one about the lotto numbers. It's only make a small difference but I think the chances are lower.

If you were to look at the statistics and see how often neighboring numbers come up next to each other, you might find that things are not necessarily equal.

UK Lotto Results: Full Draw History and Winning Numbers

Check latest UK Lotto results and full draw history (since 19 October 1994). Find past winning numbers and verify your tickets!

www.beatlottery.co.uk

Here's a lottery, I think it's the UK lottery, I'm not sure.

5th Jan they had two consecutive numbers
22nd December they had two consecutive numbers
11th December they had three consecutive numbers together
8th December they had two consecutive numbers together
4th December they had two consecutive
1st December they had one consecutive

Not bad, in the space of 40 days with 12 draws you had 4 pairs, 1 double pair and one triple. But nothing more than a triple.

What are the statistical chances of getting a double?

Well, 7 doubles in 12 draws. That's a high frequency. Chances of a triple? One in 12. Chances of a quadruple? Much less.

Lotto Statistics - Most Common Lotto Numbers

View the up to date Lotto statistics and comprehensive analysis, including number frequency graphs, most drawn numbers, jackpot history and much more.

www.national-lottery.com

Here's the frequency of the numbers. The lottery certainly isn't totally random. People get balls, they go through a process that might repeat, the machine goes through a process that repeats and perhaps there are reasons why certain numbers come out more often.

13 and 14 are the most common pair. Again, maybe this is just chance, maybe it's for some reason. Other lotteries might find it works differently. Triple numbers, 8,9,10 has appeared three times. Others have appeared twice.

Thunderball Statistics

Thunderball Statistics including the most common winning Thunderball numbers, a frequency table, the most-picked numbers and more.

www.lottery.co.uk

Bizarrely, this thunderball thing also has numbers in the teens quite high up too. Same company, I think.

Have consecutive numbers even been drawn in the lottery (like 1, 2, 3, 4, 5, 6)?

Answer (1 of 10): I don’t know if it happened but it can be interesting to calculate the probability: If the lottery has n possible numbers and you have to pick k numbers to make your ticket: There are n-k+1 possible consecutive sequences (for example a series of 4 numbers from 1 to 10 has to b...

www.quora.com

Apparently in 2016 1,2,3,4,20,21 was drawn, a quadruple.


It happens. What about five consecutive numbers?

It depends on how you approach the statistics really.

But that's specious.

That Thunderball stat site is just rude, IMO. Just trying to suck people into losing more money. They are generating noisy data from too-small a sample size to try to fool people into believing one number may have an advantage over the other, causing them to falsely inflate their expectation.

There are 39 Thunderballs, 5 balls drawn = 69 million+ combinations. How many historical drawings? 5,000? 10,000 maaaaybe?

Those noisy charts will trend to even frequencies for each number, over time.

1,2...7 has no less chance than any other 7-digit number.

 

[Fort Fun Indiana]

Whatever reason it was put there, it made the odds 50/50.

No. Sorry.

 

[Fort Fun Indiana]

What else am I missing?

(genuinely curious)

Well, I haven't seen your answers, yet.

 

[braalian]

Well, I haven't seen your answers, yet.

Well, wouldn’t the answer to all three scenarios be 1/4 since in all three you’re asking the probability of it being same color *twice*, not once?

Seems like all the other info is red herring.

 

[Fort Fun Indiana]

Then the problem is with how you write this "them" means what? I took it to mean "all the cards", you meant it to mean two cards.

"Before I lay the two cards down, I shuffle them behind my back."

Sorry for the confusion, if any.

 

[Fort Fun Indiana]

Well, wouldn’t the answer to all three scenarios be 1/4 since in all tree you’re asking the probability of being same color *twice*, not once?

Seems like all the other info is red herring.

No

1/2

1/2

1/3

 

[braalian]

No

1/2

1/2

1/3

Hmmm, but if you flip a coin twice there’s a 1/4 chance both flips will be heads.

 

[Fort Fun Indiana]

Hmmm, but if you flip a coin twice there’s a 1/4 chance both flips will be heads.

True.

And a 1/4 chance that I draw a pair of the same color.

But you get to start kicking out possibilities, if I reveal to you that one card is red.

 

[braalian]

True.

And a 1/4 chance that I draw a pair of the same color.

But you get to start kicking out possibilities, if I reveal to you that one card is red.

In a 52 card deck, sure. But if there’s infinite red and infinite black…..

 

[Fort Fun Indiana]

In a 52 card deck, sure. But if there’s infinite red and infinite black…..

Doesn't matter. The infinite deck makes it simpler math, really.

Yes, half the infinite deck is red and half is black.

 

[braalian]

I'd disagree with the last one about the lotto numbers. It's only make a small difference but I think the chances are lower.

If you were to look at the statistics and see how often neighboring numbers come up next to each other, you might find that things are not necessarily equal.

UK Lotto Results: Full Draw History and Winning Numbers

Check latest UK Lotto results and full draw history (since 19 October 1994). Find past winning numbers and verify your tickets!

www.beatlottery.co.uk

Here's a lottery, I think it's the UK lottery, I'm not sure.

5th Jan they had two consecutive numbers
22nd December they had two consecutive numbers
11th December they had three consecutive numbers together
8th December they had two consecutive numbers together
4th December they had two consecutive
1st December they had one consecutive

Not bad, in the space of 40 days with 12 draws you had 4 pairs, 1 double pair and one triple. But nothing more than a triple.

What are the statistical chances of getting a double?

Well, 7 doubles in 12 draws. That's a high frequency. Chances of a triple? One in 12. Chances of a quadruple? Much less.

Lotto Statistics - Most Common Lotto Numbers

View the up to date Lotto statistics and comprehensive analysis, including number frequency graphs, most drawn numbers, jackpot history and much more.

www.national-lottery.com

Here's the frequency of the numbers. The lottery certainly isn't totally random. People get balls, they go through a process that might repeat, the machine goes through a process that repeats and perhaps there are reasons why certain numbers come out more often.

13 and 14 are the most common pair. Again, maybe this is just chance, maybe it's for some reason. Other lotteries might find it works differently. Triple numbers, 8,9,10 has appeared three times. Others have appeared twice.

Thunderball Statistics

Thunderball Statistics including the most common winning Thunderball numbers, a frequency table, the most-picked numbers and more.

www.lottery.co.uk

Bizarrely, this thunderball thing also has numbers in the teens quite high up too. Same company, I think.

Have consecutive numbers even been drawn in the lottery (like 1, 2, 3, 4, 5, 6)?

Answer (1 of 10): I don’t know if it happened but it can be interesting to calculate the probability: If the lottery has n possible numbers and you have to pick k numbers to make your ticket: There are n-k+1 possible consecutive sequences (for example a series of 4 numbers from 1 to 10 has to b...

www.quora.com

Apparently in 2016 1,2,3,4,20,21 was drawn, a quadruple.


It happens. What about five consecutive numbers?

It depends on how you approach the statistics really.

Good point. I’ll agree that a string of consecutive numbers obviously has less chance than a string of non-consecutive ones.

But I maintain (or I think I do) that the numbers I said have just as much chance as any other *single* combination of numbers.

Times like this I wish I had taken some math courses beyond high school. Hated math with a passion, but I think I’d dig stuff like this.

 

[braalian]

Doesn't matter. The infinite deck makes it simpler math, really.

Yes, half the infinite deck is red and half is black.

How does showing one card change anything? If both halves are infinite, then showing that one is red doesn’t “take one away” from the total number of reds and thus doesn’t increase the probability of the second card being black.

 

[Fort Fun Indiana]

In a 52 card deck, sure. But if there’s infinite red and infinite black…..

Good point. I’ll agree that a string of consecutive numbers obviously has less chance than a string of non-consecutive ones.

But I maintain (or I think I do) that the numbers I said have just as much chance as anyone have a far *single* other combination of numbers.

Times like this I wish I had taken some math courses beyond high school. Hated math with a passion, but I think I’d dig stuff like this.

How does showing one card change anything?

Well, now you know they are not two black cards, if it is revealed that one of the cards is red. That is then one permutation (both black) you can kick out, of the 4 possible permutations.

 

[braalian]

Well, now you know they are not two black cards, if it is revealed that one of the cards is red. That is then one permutation (both black) you can kick out, of the 4 possible permutations.

Oh, I think I get it. So, in scenarios 1 and 2, you can disregard the first card and the question reverts to the 50/50 probability of the second card.

Bit I don’t get how shuffling the two cards in the third scenario makes a difference.