I really need an answer ASAP !! Conditional-probability

[Aetius25]

Hello, I really need an answer to this problem as soon as possible, thank you very much (Pardon my mathematical presentation I'm not an expert in maths).

The closest description of the issue can be as the following:

If n represents the number of books in a library, and x represents the number of pages in each book; what is the probability for the following event to occur:

A-E = B-D = 0

Where:

A = 1 + 2 + 3 + ... + n

B = x1 + x2 + x3 + ... + xn

C = (1+x1) + (2+x2) + (3+x3) + … + (n + xn)

D = ∑ (i+xi) " The sum of even numbers calculated in C "

E = ∑ (j+xj) " The sum of odd numbers calculated in C "

Conditions:

x (elements of B) are randomly selected from a finite set of positive integers

x > 2

i represents the number of even numbers calculated in C

j represents the number of odd numbers calculated in C

i = j = n/2 (if n = 114 then we should have 57 even numbers and 57 odd numbers in C)

n > 19

n & i & j are multiples of 19


Example:

 

[Deleted member 4993]

Hello, I really need an answer to this problem as soon as possible, thank you very much (Pardon my mathematical presentation I'm not an expert in maths).

The closest description of the issue can be as the following:

If n represents the number of books in a library, and x represents the number of pages in each book; what is the probability for the following event to occur:

A-E = B-D = 0

Where:

A = 1 + 2 + 3 + ... + n

B = x1 + x2 + x3 + ... + xn

C = (1+x1) + (2+x2) + (3+x3) + … + (n + xn)

D = ∑ (i+xi) " The sum of even numbers calculated in C "

E = ∑ (j+xj) " The sum of odd numbers calculated in C "

Conditions:

x (elements of B) are randomly selected from a finite set of positive integers

x > 2

i represents the number of even numbers calculated in C

j represents the number of odd numbers calculated in C

i = j = n/2 (if n = 114 then we should have 57 even numbers and 57 odd numbers in C)

n > 19

n & i & j are multiples of 19


Example:

View attachment 16467

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Please share your work/thoughts about this assignment.

 

[pka]

Hello, I really need an answer to this problem as soon as possible, thank you very much (Pardon my mathematical presentation I'm not an expert in maths).

The closest description of the issue can be as the following:

If n represents the number of books in a library, and x represents the number of pages in each book; what is the probability for the following event to occur:

A-E = B-D = 0

Where:

A = 1 + 2 + 3 + ... + n

B = x1 + x2 + x3 + ... + xn

C = (1+x1) + (2+x2) + (3+x3) + … + (n + xn)

D = ∑ (i+xi) " The sum of even numbers calculated in C "

E = ∑ (j+xj) " The sum of odd numbers calculated in C "

Conditions:

x (elements of B) are randomly selected from a finite set of positive integers

x > 2

i represents the number of even numbers calculated in C

j represents the number of odd numbers calculated in C

i = j = n/2 (if n = 114 then we should have 57 even numbers and 57 odd numbers in C)

n > 19

n & i & j are multiples of 19


Example:

View attachment 16467

Sorry to point this out, but truly this is a nonsense question.

 

[Aetius25]

Sorry to point this out, but truly this is a nonsense question.

Can you explain to me how is this nonsense please? the example that I shared is already existing as a fact, this is why I was told to calculate the odds of this kind of events, thank you.

 

[Aetius25]

pka, This is the full data of the example shared in the post above for more understanding:

A	B	A-E = B-D	D	E
6555	6236	0	6236	6555
n	x	(n+xn)	(i+xi)	(j+xj)
1	7	8	8
2	286	288	288
3	200	203		203
4	176	180	180
5	120	125		125
6	165	171		171
7	206	213		213
8	75	83		83
9	129	138	138
10	109	119		119
11	123	134	134
12	111	123		123
13	43	56	56
14	52	66	66
15	99	114	114
16	128	144	144
17	111	128	128
18	110	128	128
19	98	117		117
20	135	155		155
21	112	133		133
22	78	100	100
23	118	141		141
24	64	88	88
25	77	102	102
26	227	253		253
27	93	120	120
28	88	116	116
29	69	98	98
30	60	90	90
31	34	65		65
32	30	62	62
33	73	106	106
34	54	88	88
35	45	80	80
36	83	119		119
37	182	219		219
38	88	126	126
39	75	114	114
40	85	125		125
41	54	95		95
42	53	95		95
43	89	132	132
44	59	103		103
45	37	82	82
46	35	81		81
47	38	85		85
48	29	77		77
49	18	67		67
50	45	95		95
51	60	111		111
52	49	101		101
53	62	115		115
54	55	109		109
55	78	133		133
56	96	152	152
57	29	86	86
58	22	80	80
59	24	83		83
60	13	73		73
61	14	75		75
62	11	73		73
63	11	74	74
64	18	82	82
65	12	77		77
66	12	78	78
67	30	97		97
68	52	120	120
69	52	121		121
70	44	114	114
71	28	99		99
72	28	100	100
73	20	93		93
74	56	130	130
75	40	115		115
76	31	107		107
77	50	127		127
78	40	118	118
79	46	125		125
80	42	122	122
81	29	110	110
82	19	101		101
83	36	119		119
84	25	109		109
85	22	107		107
86	17	103		103
87	19	106	106
88	26	114	114
89	30	119		119
90	20	110	110
91	15	106	106
92	21	113		113
93	11	104	104
94	8	102	102
95	8	103		103
96	19	115		115
97	5	102	102
98	8	106	106
99	8	107		107
100	11	111		111
101	11	112	112
102	8	110	110
103	3	106	106
104	9	113		113
105	5	110	110
106	4	110	110
107	7	114	114
108	3	111		111
109	6	115		115
110	3	113		113
111	5	116	116
112	4	116	116
113	5	118	118
114	6	120	120

 

[Dr.Peterson]

Hello, I really need an answer to this problem as soon as possible, thank you very much (Pardon my mathematical presentation I'm not an expert in maths).

The closest description of the issue can be as the following:

If n represents the number of books in a library, and x represents the number of pages in each book; what is the probability for the following event to occur:

A-E = B-D = 0

Where:

A = 1 + 2 + 3 + ... + n

B = x1 + x2 + x3 + ... + xn

C = (1+x1) + (2+x2) + (3+x3) + … + (n + xn)

D = ∑ (i+xi) " The sum of even numbers calculated in C "

E = ∑ (j+xj) " The sum of odd numbers calculated in C "

Conditions:

x (elements of B) are randomly selected from a finite set of positive integers

x > 2

i represents the number of even numbers calculated in C

j represents the number of odd numbers calculated in C

i = j = n/2 (if n = 114 then we should have 57 even numbers and 57 odd numbers in C)

n > 19

n & i & j are multiples of 19

I think what we need is to figure out what event you are asking about. (You admitted your presentation was bad, so we have to correct it.)

What does A-E = B-D = 0 mean? I would take it to mean A=E and B=D; but in what sense is that an "event"? And are all the "conditions" you list meant to be part of the definition of the event?

Looking at your definitions of A through E (in which many variables appear to have subscripts that you have not formatted as such (despite your heavy use of formatting), it looks like A+B = C, and D and E are evidently meant to be, respectively, sums of the even terms and the odd terms of the sum in C, which I suppose means not the terms with even or odd index, but terms whose values are even or odd. Therefore D+E = C. Am I right? So if A=E, then B=D necessarily.

You've indicated that x is a set of n data points x_k, each of which is a positive integer; are they distinct, or can some have the same value? You call them "elements of B"; you mean they are the terms of the sum B (that is, B is the sum of elements of x). But then you say x > 2; what does that mean? (A set of data doesn't have a numerical value.) Possibly you mean that each element of x (that is, each x_k) is greater than 2.

But then you say that i and j are each n/2, which means that somehow this "random" set of data is such that exactly half of the numbers "k + x_k" are even, and half are odd. How does that happen?

But then looking at the example, you are not consistently using n, i, and j as total numbers of data points, as you'd said, but use each of them as I have used k.

My intention is not to criticize your notation, but to figure out what the event is. What you want might be a lot clearer if you told us what it all means. In terms of books and pages, what is the significance of this event? Why did you choose such an odd "event"? And how are the numbers x selected "randomly"? Are you selecting books with equal probability, or what? In order to have a probability at all, you need a population and a sampling method.

As I work through this, I get the feeling that you have a particular set of numbers and want to say that it is extremely unlikely for the properties you have found to occur. If so, that is a meaningless question, because when you choose a data set first, and then choose an event after the fact, there is no randomness at all. For a look at this issue, if that is the case, you might read this (on my blog, where I discuss past answers on a different site).