[Quiz] Answer the Bitcoin question and earn merits! #2

[BlackHatCoiner]

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Short introduction for anyone who missed the first quiz:

I decided to start these forum quiz-series, where I'll be asking questions of educational character, to improve the average user's knowledge around Bitcoin. The questions will mostly be technical and historical. To create an incentive, I will generously merit the first person who replies with the correct answer. If that is not good enough incentive, I'll create a leaderboard!

• Your answer needs to be explanatory. Not just a yes-no or a single number.
• If nobody finds the answer until the cut-off date, I will submit it.
• Have fun! It's a game.  

The first question was a tribute to the whitepaper. Now let's see how good we are at math.


Question: What is the chance of having exactly three blocks mined within the next 10 minutes? You can assume that a new block is mined every 10 minutes on average.

Cut-off date: 27/03/2024.

[1714252719]

1714252719

[1714252719]

1714252719

[Mia Chloe]

Since a  block is mined every 10 minutes the probability of mining 3 blocks in 10 minutes will be
Number of possible blocks -->1
Number of required block --> 3
 Keeping time constant (10minutes)
P=1/3
P=0.33
Or 33.33%

[BlackHatCoiner]

P=1/3
P=0.33
Or 33.33%

Sometimes, for more than 10 minutes, no block is found. So, the probability of finding one block within the next 10 minutes is not 100%. 

[Mia Chloe]

P=1/3
P=0.33
Or 33.33%

Sometimes, for more than 10 minutes, no block is found. So, the probability of finding one block within the next 10 minutes is not 100%. 

You are correct I'm still working on it though guess I will have to use poissons  ratio

[rachael9385]

Question: What is the chance of having exactly three blocks mined within the next 10 minutes? You can assume that a new block is mined every 10 minutes on average.

Hmm. Am not a good mathematics student but I would like to try my best on this.
If 3 blocks was mined 10 minutes, that means each transaction would be mined within  1/10^3 and 0.0027 per transaction.
1/10^3 gotten from the λ and the 0.0027 is 1/10^3

[Ricardo11]

I am explaining your question mathematically,


We know the formula of probability is :- possibility=  (Number of favorable outcomes of events / Number of possible outcomes)

suppose :- Number of favorable outcomes of events {P} and Number of possible outcomes {X}

As this as this:- Number of favorable outcomes of events(P):- 10
Number of possible outcomes(X):- 3

Therefore :- possibility= (P/X)

= (10/3)

=30%


With a 30% chance, since a new block is mined every 10 minutes, it is possible to mine about 3 blocks every 10 minutes. And in 10 minutes the chance of having exactly three blocks mined is 30% or (10/3)%.

[Wapfika]

Here is my final solution
The time was same in both cases so time is constant.
0.008298

I don’t want to hijack your submission but I think you substituted wrong value to your -lambda instead of 1 you use 3 that’s why it gives you a wrong answer on this computation.

But using Poison Distribution Method will give 6.13% if you correctly substitute the value. I’m not sure if this computation will be accurate on Bitcoin mining since I don’t have enough knowledge on this area.

[Mia Chloe]

I don’t want to hijack your submission but I think you substituted wrong value to your -lambda instead of 1 you use 3 that’s why it gives you a wrong answer on this computation.

But using Poison Distribution Method will give 6.13% if you correctly substitute the value. I’m not sure if this computation will be accurate on Bitcoin mining since I don’t have enough knowledge on this area.

Thanks for the heads up

I mistakenly substituted 3 instead of 1

[Aanuoluwatofunmi]

Poison Distribution explains it all

If the hashrate is not constant and we experience a memoryless event through the poison process, which describe the number of blocks that can be possily mined at a particular given time interval, Poinson distribution explains how such an event could occur on a multiple times, you can learn more from these https://careerfoundry.com/en/blog/data-analytics/what-is-poisson-distribution/

[Alphakilo]

The first question was a tribute to the whitepaper. Now let's see how good we are at math.


Question: What is the chance of having exactly three blocks mined within the next 10 minutes? You can assume that a new block is mined every 10 minutes on average.

Cut-off date: 27/03/2024.

Not like I have a choice but I preferred the first question better

These are very critical mining questions with a mix of math.
I am terrible at math.

I will return to this thread after the cut-off date - 27/03/2024 and try just study the answer of whoever gets the quiz correctly. Just maybe in the future I will be able to participate.

[Judith87403]

Question: What is the chance of having exactly three blocks mined within the next 10 minutes? You can assume that a new block is mined every 10 minutes on average.

Cut-off date: 27/03/2024.

I'm using mathematics to explain the question:

probability 1/10  ...K= P(3:1) that (3 blocks per minute) = (e^-1-1^3)/3! =1/e.6 = 0.0613 ~ 6.13

^ is a power function
mean ^-1 ...-1 is to the function "e"  same as ^3 to the function "1"

[Etranger]

I don’t want to hijack your submission but I think you substituted wrong value to your -lambda instead of 1 you use 3 that’s why it gives you a wrong answer on this computation.

But using Poison Distribution Method will give 6.13% if you correctly substitute the value. I’m not sure if this computation will be accurate on Bitcoin mining since I don’t have enough knowledge on this area.

Thanks for the heads up

I mistakenly substituted 3 instead of 1

I also got the same result using this formula. However, the word “exactly” in the BlackHatCoiner`s assignment confuses me. After all, this implies that exactly 3 blocks and no more should be mined in 10 minutes, and that the situation where 3 were mined and the fourth was already started to be mined is not suitable, as far as I understand. That is, after exactly ten minutes, exactly three blocks should be mined, and the extraction of the fourth should fall on the eleventh minute. And if my thoughts are correct, then Poison Distribution formula does not take this into account and the probability is calculated incorrectly, because it is greater than it actually is.

[Amphenomenon]

I wrote mine as a code in python, to be Frank my code is not professional _{i`m still working on that}

Code:

import math
Parameter = 1 
RandomNumber = 3
EulerNumber = 2.71828

Probability = (Parameter ** RandomNumber ) * (EulerNumber ** (-Parameter)) / math.factorial(RandomNumber)
RoundedProbability = round(Probability, 4)
Inpercentage = str(RoundedProbability * 100)
print ('The chance of having exactly three blocks mined within the next 10 minutes = ', 
       RoundedProbability, 'or', Inpercentage + '%')

Poisson distribution was also spoken about on the bitcoin whitepaper in page 7 even in regards to your previous question

[CryptoHeadlineNews]

Question: What is the chance of having exactly three blocks mined within the next 10 minutes? You can assume that a new block is mined every 10 minutes on average.

Since Probability simply means the extent to which an event likely to occur, and we all know that it takes approximately 10 minutes for each block to be mined, I think the answer to this is what I will be giving in the calculation down below.

FORMULA FOR PROBABILITY

P(A) = Number of times A occur / Total number of possible outcomes


Where;
Number of times A occur = 10
Total number of possible outcomes = 3
Probability = ?


P(A) = (10 / 3) = 3.33

[BlackHatCoiner]

If 3 blocks was mined 10 minutes, that means each transaction would be mined within  1/10^3 and 0.0027 per transaction.
1/10^3 gotten from the λ and the 0.0027 is 1/10^3

These are some non-understandable math. Why 10^3, how did you work out 0.0027 and what does it mean?

We know the formula of probability is :- possibility=  (Number of favorable outcomes of events / Number of possible outcomes)

That's not the correct formula to use. Your formula makes sense in finite sets. For example, the odds of getting an even number from a dice roll.

Code:

{Total of even integers from 1 to 6} / {Total integers from 1 to 6} = 3 / 6 = 0.5

The set of all possible outcomes in the Bitcoin network within 10 minutes is infinite.


Before I unveil the answer, I want to leave the thread for a few hours. Maybe someone wants to correct the replies above. 

[Ricardo11]

The probability of mining a new block every 10 minutes is about 1/10 or 10% on average.

 If each block has a 10% chance of being mined, then the probability of mining three blocks is:

 (10% * 10% * 10%) = 0.1 * 0.1 * 0.1 = 0.001

 Or 0.1%, ie 1/1000. So the probability of mining three blocks in the next 10 minutes is about 0.1% or 1/1000.

Otherwise,,,

Since there is a binomial probability for each event (yes or no), the probability will be the average position of the numbers.

 Given its value, the binomial probability for each event will be 1/2.

  Then the probabilities for the first three events would be:

 (1/2) * (1/2) * (1/2) = 1/8

[AmaGold70]

Question: What is the chance of having exactly three blocks mined within the next 10 minutes? You can assume that a new block is mined every 10 minutes on average.

To calculate the probability of having exactly three blocks mined within the next 10 minutes (which is almost impossible) I used the poisson formula and I got p(3;1) =0.0613
So I'd say that there's a 6.13% chance of having exactly three blocks mined within the next 10 minutes.

I could have loved to explain how I got my answer in details but my keyboard isn't giving me every thing I need to type.

The poisson formula looks like this, p(x;a) = (e^(-a) *a^x) / x!

I used "a" to replace the symbol I couldn't find in my keyboard.

It seems newbies aren't allowed to send a picture here because I did my calculations in my notebook as it would have been easier for me to drop a picture of my calculations. I may be wrong though with my answer but am delighted to participate.

[philipma1957]

actually this is a good question.

as the 6.13 percent answer left out all the chances above 3 blocks.

so it is close but no cigar.

if you did  if for

4 blocks you would get a smaller number.  say 1 percent
5 blocks you would get a smaller number than 1 percent say .1 percent

you could do that for

4,5,6,7,8,9,10 and maybe that gives a close enough estimate for more than 3 blocks maybe it is 1.4%

then take the 6.13-1.4 and get 4.73%


not perfect but if you extend to 20 blocks in 10 minutes it would be very accurate.

So I say

Poisson distribution for 3 blocks = 6.13

then add poisson for
4
5
6
7
8
9
10  subtract from poisson for 3 and very accurate

more accurate

poisson
for
11
12
13
14
15
16
17
18
19
20 add to 4-10 and subtract that from poisson for 3

since the possibility is endless but unlikely I would accept

poisson for 3 -  poisson's  for (4+5+6+7+8+9+10) as close enough

[Cityhunter34]

 Or 0.1%, ie 1/1000. So the probability of mining three blocks in the next 10 minutes is about 0.1% or 1/1000

I got the same thing.
To find the probability of having exactly three blocks mined, I multiplied the probability of a single block being mined three times, that is, 1/10 * 1/10 * 1/10 = 1/1000

The chance of having exactly three blocks mined in 10 minutes is 0.001

[Mia Chloe]

actually this is a good question.

as the 6.13 percent answer left out all the chances above 3 blocks.

so it is close but no cigar.

I actually thought about this but I didn't make use of values ≥3 because the question asked was for exactly 3 blocks.

If not I would simply calculate that for 2 blocks and 1 block and then subtract the value from 1 to get that for the number of possible mined blocks geater than of equal to 3 since;
Pr(<2 blocks) + Pr(≥3 blocks) = 1
So  Pr(≥3 blocks) = 1- Pr(<2 blocks)
Since Pr(≥3 blocks)  more like tends to infinity and thus would be more difficult to compute as you would have to solve for the probability of 3,4 ,5,6,7........ Till infinity the more Pr(≥3 blocks) outcomes you compute, the more accurate your probability.