Exam question 1 · "I'm due a win": the gambler's fallacy

Identify the principal error in the assertion that tails is "due" after five consecutive heads with a fair coin.

Mova's choice: option 3 · The right answer: option 3 · right ✓ · Who acts: you, assertion · What happens: identify, be · To what, where: principal error, assertion

This is exam question 1 of lesson 171 «"I'm due a win": the gambler's fallacy» of the world course of Mova's primary school, asked in stiff, formal language. The page gives the question's syntax tree — a dependency tree in the style of Universal Dependencies — and its pragmatics clause by clause, then the 4 options as the student saw them, each with its tree and pragmatics. Every text is parsed by Mova itself. How the student answered it, with the score of every option and why: the test at school.

The question

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	Identify	identify	VERB	Mood=Imp VerbForm=Fin	root	root
2	the	the	DET	Definite=Def PronType=Art	4 error	det
3	principal	principal	ADJ	Degree=Pos	4 error	amod
4	error	error	NOUN	Number=Sing	1 Identify	obj
5	in	in	ADP	_	7 assertion	case
6	the	the	DET	Definite=Def PronType=Art	7 assertion	det
7	assertion	assertion	NOUN	Number=Sing	1 Identify	obl
8	that	that	PRON	PronType=Rel	12 due	nsubj
9	tails	tail	NOUN	Number=Plur	12 due	nsubj
10	is	be	AUX	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	12 due	cop
11	"	"	PUNCT	_	12 due	punct
12	due	due	ADJ	Degree=Pos ExtPos=ADP	7 assertion	acl:relcl
13	"	"	PUNCT	_	12 due	punct
14	after	after	ADP	_	17 heads	case
15	five	five	NUM	NumForm=Word NumType=Card	17 heads	nummod
16	consecutive	consecutive	ADJ	Degree=Pos	17 heads	amod
17	heads	head	NOUN	Number=Plur	1 Identify	obl
18	with	with	ADP	_	21 coin	case
19	a	a	DET	Definite=Ind PronType=Art	21 coin	det
20	fair	fair	ADJ	Degree=Pos	21 coin	amod
21	coin	coin	NOUN	Number=Sing	1 Identify	obl
22	.	.	PUNCT	_	1 Identify	punct

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	identify	imperative	you not said here	the principal error		the assertion	after five consecutive heads	with a fair coin	vn characterize-29.2-1-1 «NP V NP S_ING»: agent=Agent error=Theme
2	is in a quote	present	the assertion					due property	tree rules

One row per clause the reader finds. «not said here»: a role filled from the clause above. «roles by»: a VerbNet class and frame when one fits the verb, else the reader's rules on the tree.

The options

Option 1

The coin is likely to be weighted

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	The	the	DET	Definite=Def PronType=Art	2 coin	det
2	coin	coin	NOUN	Number=Sing	4 likely	nsubj
3	is	be	AUX	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	4 likely	cop
4	likely	likely	ADJ	Degree=Pos	root	root
5	to	to	PART	_	7 weighted	mark
6	be	be	AUX	VerbForm=Inf	7 weighted	aux:pass
7	weighted	weight	VERB	Tense=Past VerbForm=Part Voice=Pass	4 likely	xcomp

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	is	present	the coin					likely property	tree rules
2	weight	to-infinitive · passive	the coin not said here						vn equip-13.4.2-1-1 «NP.theme V NP»

Option 2

Five heads constitute an insufficient sample

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	Five	five	NUM	NumForm=Word NumType=Card	2 heads	nummod
2	heads	head	NOUN	Number=Plur	3 constitute	nsubj
3	constitute	constitute	VERB	Mood=Ind Number=Plur Person=3 Tense=Pres VerbForm=Fin	root	root
4	an	a	DET	Definite=Ind PronType=Art	6 sample	det
5	insufficient	insufficient	ADJ	Degree=Pos	6 sample	amod
6	sample	sample	NOUN	Number=Sing	3 constitute	obj

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	constitute	present	Five heads	a insufficient sample					vn comprise-107.2-1 «NP V NP»: agent=Theme sample=Pivot

Option 3 · ← Mova's choice · ✓ the right answer

The coin retains no memory of prior outcomes

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	The	the	DET	Definite=Def PronType=Art	2 coin	det
2	coin	coin	NOUN	Number=Sing	3 retains	nsubj
3	retains	retain	VERB	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	root	root
4	no	no	DET	PronType=Neg	5 memory	det
5	memory	memory	NOUN	Number=Sing	3 retains	obj
6	of	of	ADP	_	8 outcomes	case
7	prior	prior	ADJ	Degree=Pos	8 outcomes	amod
8	outcomes	outcome	NOUN	Number=Plur	5 memory	nmod

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	retain	present	the coin	no memory of prior outcomes					tree rules

Option 4

Tails cannot occur after heads

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	Tails	tail	NOUN	Number=Plur	4 occur	nsubj
2	can	can	AUX	VerbForm=Fin	4 occur	aux
3	not	not	PART	Polarity=Neg	4 occur	advmod
4	occur	occur	VERB	VerbForm=Inf	root	root
5	after	after	ADP	_	6 heads	case
6	heads	head	NOUN	Number=Plur	4 occur	obl

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	not occur	can	Tails				after heads		vn occur-48.3-1 «NP V»: agent=Theme

Text: the tests of Mova's primary school, written for Mova (world/data/school/), as the course runner gave them to the student. Trees: Mova's own parse — the en model on the CPU, when the site is built — not checked by a teacher; they may be wrong. Frames: Mova's frames reader (prag), each text read on its own. Elamur Cosmic License.

This page in Markdown → https://md.mova.elamur.ai/free/en/corpora/questions/world/171-im-due-a-win-the-gamblers-fallacy/e1/