@DavidM_yeg @griffin30007 @nblr
This is weirdly hostile considering the word "or" doesn't appear anywhere prior in this chain of replies
Ava
@faelif@mathstodon.xyz
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4.5.8
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer.
Open to follow requests, I just like to know who's following me.
Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov
Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657
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Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
@faelif@mathstodon.xyz
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5d ago
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Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
@faelif@mathstodon.xyz
·
Apr 10, 2026
I've been keeping myself topically engaged!
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Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
@faelif@mathstodon.xyz
·
Apr 01, 2026
Did no one think Integrity flying away from the US was bad optics?
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Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
@faelif@mathstodon.xyz
·
Apr 08, 2025
@skewray @vpunt
I don't think your probability formula quite works.
Suppose we're tossing coins and waiting for the sub-sequence TT. We'd like to know the chance that it happens on our fourth toss: n = 4, m = 2, p = ¼. There are two sequences that would result in n=4:
HHTT
THTT
Any other sequence would succeed too early (e.g. HTTT) or not result in success (e.g. HTHT). So I think for n=4 the probability would be 2/16, which is definitely not (1-¼)¹(¼) = 3/16.
Note that there are three sequences that would give n=4 for the sub-sequence HT:
HHHT
THHT
TTHT
which would give the 3/16 from your formula - so I no longer think that the probability can be independent of the sub-sequence chosen.
I don't think your probability formula quite works.
Suppose we're tossing coins and waiting for the sub-sequence TT. We'd like to know the chance that it happens on our fourth toss: n = 4, m = 2, p = ¼. There are two sequences that would result in n=4:
HHTT
THTT
Any other sequence would succeed too early (e.g. HTTT) or not result in success (e.g. HTHT). So I think for n=4 the probability would be 2/16, which is definitely not (1-¼)¹(¼) = 3/16.
Note that there are three sequences that would give n=4 for the sub-sequence HT:
HHHT
THHT
TTHT
which would give the 3/16 from your formula - so I no longer think that the probability can be independent of the sub-sequence chosen.
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Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
@faelif@mathstodon.xyz
·
Apr 07, 2025
@skewray
The instigating question was figuring out the expected time for the sequence to occur, so I suppose it doesn't matter either way.
The instigating question was figuring out the expected time for the sequence to occur, so I suppose it doesn't matter either way.
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Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
Ava
@faelif@mathstodon.xyz
faelif aka Ava. 19. UK. Maths student at Cambridge; occasional programmer. Open to follow requests, I just like to know who's following me. Now reading: Carpet People by Terry Pratchett, and Foundation and Empire by Isaac Asimov Profile image source: https://safebooru.org/index.php?page=post&s=view&id=6213657 GNU Terry Pratchett
mathstodon.xyz
@faelif@mathstodon.xyz
·
Apr 07, 2025
Suppose I have a random event with k possible outcomes of equal probability. What distribution (if any) describes the probability of obtaining a specific sequence of length m after n events?
#probability #probabilitydistribution #statistics
#probability #probabilitydistribution #statistics
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