Exam question 3 · Gambling and honesty with change

Which of the following statements most accurately characterises the probability of a fair coin falling heads upon the sixth toss, five heads having previously been obtained?

Mova's choice: option 2 · The right answer: option 3 · wrong ✗ · Who acts: fair coin, five heads · What happens: follow, characteris, fall, have, obtain · To what, where: probability, heads

This is exam question 3 of lesson 40 «Gambling and honesty with change» of the money 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	Which	which	PRON	PronType=Rel	8 characterises	nsubj
2	of	of	ADP	_	5 statements	case
3	the	the	DET	Definite=Def PronType=Art	5 statements	det
4	following	follow	VERB	VerbForm=Ger	5 statements	amod
5	statements	statement	NOUN	Number=Plur	8 characterises	obl
6	most	most	ADV	Degree=Sup	7 accurately	advmod
7	accurately	accurately	ADV	_	8 characterises	advmod
8	characterises	characteris	VERB	Mood=Ind Number=Sing Person=3 Tense=Pres VerbForm=Fin	root	root
9	the	the	DET	Definite=Def PronType=Art	10 probability	det
10	probability	probability	NOUN	Number=Sing	8 characterises	obj
11	of	of	ADP	_	14 coin	case
12	a	a	DET	Definite=Ind PronType=Art	14 coin	det
13	fair	fair	ADJ	Degree=Pos	14 coin	amod
14	coin	coin	NOUN	Number=Sing	10 probability	nmod
15	falling	fall	VERB	VerbForm=Ger	14 coin	acl
16	heads	head	NOUN	Number=Plur	15 falling	obj
17	upon	upon	ADP	_	20 toss	case
18	the	the	DET	Definite=Def PronType=Art	20 toss	det
19	sixth	sixth	ADJ	Degree=Pos	20 toss	amod
20	toss	toss	NOUN	Number=Sing	15 falling	obl
21	,	,	PUNCT	_	23 heads	punct
22	five	five	NUM	NumForm=Word NumType=Card	23 heads	nummod
23	heads	head	NOUN	Number=Plur	10 probability	conj
24	having	have	VERB	VerbForm=Ger	23 heads	acl
25	previously	previously	ADV	_	27 obtained	advmod
26	been	be	AUX	Tense=Past VerbForm=Part	27 obtained	aux:pass
27	obtained	obtain	VERB	Tense=Past VerbForm=Part Voice=Pass	24 having	xcomp
28	?	?	PUNCT	_	8 characterises	punct

#	verb	tense, mood	who	what, whom	other	roles by
1	follow	gerund				vn occur-48.3-1 «NP V»: agent=Theme
2	characteris	present		the probability of a fair coin and five heads	of the following statements; accurately property	tree rules
3	fall	gerund	a fair coin not said here	heads	upon the sixth toss	vn become-109.1-1 «NP V ADJ»: agent=Patient head=Result
4	have	gerund	five heads not said here			tree rules
5	obtain	participle · passive	five heads not said here		previously property	vn obtain-13.5.2-1 «NP.asset V NP»

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

One in thirty-two, the preceding tosses being taken into account

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	One	one	NUM	NumForm=Word NumType=Card	root	root
2	in	in	ADP	_	3 thirty	case
3	thirty	thirty	NUM	NumForm=Word NumType=Card	1 One	nmod
4	-	-	PUNCT	_	5 two	punct
5	two	two	NUM	NumForm=Word NumType=Card	3 thirty	conj
6	,	,	PUNCT	_	11 taken	punct
7	the	the	DET	Definite=Def PronType=Art	9 tosses	det
8	preceding	precede	VERB	VerbForm=Ger	9 tosses	amod
9	tosses	toss	NOUN	Number=Plur	11 taken	nsubj:pass
10	being	be	AUX	Tense=Pres VerbForm=Part	11 taken	aux:pass
11	taken	take	VERB	Tense=Past VerbForm=Part Voice=Pass	1 One	parataxis
12	into	into	ADP	_	13 account	case
13	account	account	NOUN	Number=Sing	11 taken	obl

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	precede	gerund							vn contiguous_location-47.8 «NP V NP»: agent=Theme
2	take	gerund · passive		the preceding tosses		account			vn bring-11.3 «NP V NP PP.destination»: subject=Theme into account=Destination

Option 2 · ← Mova's choice

Certainty, a sixth head being inevitable

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	Certainty	certainty	NOUN	Number=Sing	7 inevitable	nsubj
2	,	,	PUNCT	_	5 head	punct
3	a	a	DET	Definite=Ind PronType=Art	5 head	det
4	sixth	sixth	ADJ	Degree=Pos	5 head	amod
5	head	head	NOUN	Number=Sing	1 Certainty	conj
6	being	be	AUX	Tense=Pres VerbForm=Part	7 inevitable	cop
7	inevitable	inevitable	ADJ	Degree=Pos	root	root

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	is	gerund	Certainty and a sixth head					inevitable property	tree rules

Option 3 · ✓ the right answer

One in two, each toss being independent of those preceding it

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	One	one	NUM	NumForm=Word NumType=Card	root	root
2	in	in	ADP	_	3 two	case
3	two	two	NUM	NumForm=Word NumType=Card	1 One	nmod
4	,	,	PUNCT	_	8 independent	punct
5	each	each	DET	PronType=Tot	6 toss	det
6	toss	toss	NOUN	Number=Sing	8 independent	nsubj
7	being	be	AUX	Tense=Pres VerbForm=Part	8 independent	cop
8	independent	independent	ADJ	Degree=Pos	1 One	amod
9	of	of	ADP	_	10 those	case
10	those	that	PRON	Number=Plur PronType=Dem	8 independent	obl
11	preceding	precede	VERB	VerbForm=Ger	10 those	acl
12	it	it	PRON	Case=Acc Gender=Neut Number=Sing Person=3 PronType=Prs	11 preceding	obj

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	is	gerund	each toss					of those; independent property	tree rules
2	precede	gerund		toss					vn contiguous_location-47.8 «NP V NP»: agent=Theme it=Co-Theme

Option 4

Impossibility, tails being obligatorily due

The words, one row each (CoNLL-U)

#	word	lemma	UPOS	features	head	relation
1	Impossibility	impossibility	NOUN	Number=Sing	3 tails	compound
2	,	,	PUNCT	_	1 Impossibility	punct
3	tails	tail	NOUN	Number=Plur	6 due	nsubj
4	being	be	AUX	Tense=Pres VerbForm=Part	6 due	cop
5	obligatorily	obligatorily	ADV	_	6 due	advmod
6	due	due	ADJ	Degree=Pos	root	root

#	verb	tense, mood	who	what, whom	to whom	where	when	other	roles by
1	is	gerund	Impossibility tails					due, obligatorily property	tree rules

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.

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