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Mathsss reality riddle

 
 
Reply Fri 27 Apr, 2012 11:27 pm
In audience poll out of 100 people, 40 poll for answer as A choice in which 30 poll thinking A is wrong choice. 20 poll for B choice, in which 8 poll thinking B is wrong. 30 poll for choice C , in which 15 thinking C is wrong. 10 poll for choice D, in which 3 thinking D is wrong. If contestant came to know this, then based on correct high percentage, which choice is correct
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Type: Question • Score: 0 • Views: 1,811 • Replies: 24
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markr
 
  1  
Reply Sat 28 Apr, 2012 10:51 am
@sandy111,
I get:
D: 29.3
B: 29.1
C: 27.2
A: 14.4
sandy111
 
  1  
Reply Tue 1 May, 2012 12:20 am
@markr,
its wrong.....tell me how u come to this solution
markr
 
  1  
Reply Tue 1 May, 2012 08:52 pm
@sandy111,
What we know:
10 out of 40 people think A is the answer. At least 64 people think A is not the answer.
12 out of 20 people think B is the answer. At least 40 people think B is not the answer.
15 out of 30 people think C is the answer. At least 44 people think C is not the answer.
7 out of 10 people think D is the answer. At least 40 people think D is not the answer.

There are 30 people from the first group, 8 people from the second group, 15 people from the third group, and 3 people from the fourth group that all we know about them is one answer they don't think is correct. I assigned these people to the other three choices based on a pro-rating scheme that is based on their approval percentages in their groups.

For instance, the 30 people from the first group who thought A was incorrect were divided up among B, C, and D according to these proportions: (12/20) / (12/20 + 15/30 + 7/10), (15/30) / (12/20 + 15/30 + 7/10), and (7/10) / (12/20 + 15/30 + 7/10). I used the same method for the other three groups.

If you don't try to assign the unknown votes and only go with what you know for certain, you could use:
A: 10/74 = 13.5
B: 12/15 = 23.1
C: 15/59 = 25.4
D: 7/47 = 14.9

How would you do it?


DrewDad
 
  1  
Reply Wed 2 May, 2012 07:31 am
@markr,
I read it as 40 people think A is the correct answer, 30 people think A is wrong, and 30 people have no opinion.

I don't understand "correct high percentage," though.

Should we calculate it as 40/(40+30) to get 57% of respondents think that A is correct?

In that case, D is correct, as 77% of people who have an opinion about D think it is the correct answer.

But there are 100 votes for the various answers, and only 56 votes against answers. Apparently, voting against answers was optional.



DrewDad
 
  1  
Reply Wed 2 May, 2012 07:40 am
@DrewDad,
I don't get the bit about voting against answers. Presumably, if a respondent is voting for an answer, they automatically think the other answers are wrong.
sandy111
 
  1  
Reply Wed 2 May, 2012 07:52 am
@sandy111,
In fav of A = 10/40 = .25
B = 12/20 = 0.6
C= 15/30 = 0.5
D = 7/10 = 0.7
Thus ,
Not favouring A = (1-0.25) = 0.75
Favouring B = 0.6
Fav C= 0.5
Fav D = 0.7

Thus,Final Not Fav. A = (0.75) (0.6) (0.5) (0.7) =0.157

Thus, Fav A = 1- 0.157 = 0.85


Similarly,
Fav B = 1-0.035 = .96

FAv C = 0.94
Fav D = 0.97

Answer is D= 0.97..............Please Comment...
sandy111
 
  1  
Reply Wed 2 May, 2012 07:52 am
@markr,
In fav of A = 10/40 = .25
B = 12/20 = 0.6
C= 15/30 = 0.5
D = 7/10 = 0.7
Thus ,
Not favouring A = (1-0.25) = 0.75
Favouring B = 0.6
Fav C= 0.5
Fav D = 0.7

Thus,Final Not Fav. A = (0.75) (0.6) (0.5) (0.7) =0.157

Thus, Fav A = 1- 0.157 = 0.85


Similarly,
Fav B = 1-0.035 = .96

FAv C = 0.94
Fav D = 0.97

Answer is D= 0.97..............Please Comment...
sandy111
 
  1  
Reply Wed 2 May, 2012 07:59 am
@DrewDad,
There are three houses A B C on an arc of radius 1km. Rooney moves from A to B by shortest distance which is 1km and then B to C which is 2km. If he come back from C to A what is shortest distance he covered from C to A.
markr
 
  2  
Reply Wed 2 May, 2012 09:13 am
@sandy111,
A, B, and C are on the vertices of a regular hexagon with sides equal to 1. B and C are opposite each other (diameter). The distance between A and C is the length of a short diagonal on the hexagon. Should be sqrt(3).
sandy111
 
  1  
Reply Wed 2 May, 2012 09:47 am
@markr,
No...not like that
0 Replies
 
DrewDad
 
  1  
Reply Wed 2 May, 2012 10:12 am
@sandy111,
We know that B to C passes through the center of the circle, since that's the only chord that can have a length of 2 km.

Therefore, the points A, B, and the center of the triangle (call it D) form an equilateral triangle with lengths 1 km.

This tells us that angle B in the triangle ABD is 60 degrees. This also means that the angle B in triangle ABC is 60 degrees.

So we have a triangle ABC, with sides AB = 1 km, BC = 2 km, and angle B 60 degrees.

Angle-side-angle calculation to five decimal places gives us 1.73205 km for line AC.

Incidentally, the square of 1.73205 is 2.9999972025, so I must assume that the precise measurement is sqrt(3).... which means MarkR was absolutely correct.

And a much more elegant solution, I might add.

sandy111
 
  1  
Reply Wed 2 May, 2012 10:27 am
@DrewDad,
If B to C is 1km, now what would be answer?
DrewDad
 
  1  
Reply Wed 2 May, 2012 11:13 am
@sandy111,
Continuing to call the center point of the circle "D," we see:

Angle B in ABD is still 60 degrees.

Angle B in DBC is 60 degrees as well.

So we have two sides AB and BC that are each 1 km, and we see that angle B in ABC is 120 degrees.

Side-angle-side/law of cosines calculation from there.

http://www.calculatorsoup.com/calculators/geometry-plane/triangle-theorems.php

~1.73205 km or sqrt(3) km.
sandy111
 
  1  
Reply Wed 2 May, 2012 11:21 am
@DrewDad,
If two chords are on one side of semicircle, then wats d line joining them.When none passes through center of circle?
markr
 
  1  
Reply Wed 2 May, 2012 01:12 pm
@sandy111,
In a circle of radius 1, the only chords that have length 2 are diameters. Diameters always pass through the center of the circle.
0 Replies
 
DrewDad
 
  1  
Reply Wed 2 May, 2012 01:20 pm
@sandy111,
Are we still talking triangles?

From what you wrote, I think you mean: If two chords share an endpoint, then a third chord will create a triangle. Show how to calculate the length of the third side if you are given the lengths of the first two chords.

Is that correct, or do you have something else in mind?
0 Replies
 
DrewDad
 
  1  
Reply Wed 2 May, 2012 01:22 pm
@sandy111,
sandy111 wrote:
Please Comment...

Frankly, I don't understand your methodology.
0 Replies
 
markr
 
  1  
Reply Wed 2 May, 2012 01:27 pm
@DrewDad,
Quote:
I read it as 40 people think A is the correct answer, 30 people think A is wrong, and 30 people have no opinion.

I don't understand "correct high percentage," though.

Should we calculate it as 40/(40+30) to get 57% of respondents think that A is correct?

In that case, D is correct, as 77% of people who have an opinion about D think it is the correct answer.

But there are 100 votes for the various answers, and only 56 votes against answers. Apparently, voting against answers was optional.


I read it this way (based on Sandy's "solution" I think this is correct):
Divide 100 people into 4 groups of 40, 20, 30, and 10.
Ask the first group if A is correct (y/n).
Ask the second group if B is correct (y/n).
Same for the last two groups.

For choice A, we know that 10 people (out of the group of 40) think it is correct. We also know that 30 people out of the group of 40, 12 people out of the group of 20, 15 people out of the group of 30, and 7 people out of the group of 10 think it is incorrect.

What we don't know is what the people in each group that said "incorrect" think is the correct answer. I attempted to distribute these unknown votes among the possible choices based on pro-rating the sampling done in the 4 subgroups.
markr
 
  1  
Reply Wed 2 May, 2012 01:39 pm
@sandy111,
Quote:
In fav of A = 10/40 = .25
B = 12/20 = 0.6
C= 15/30 = 0.5
D = 7/10 = 0.7
Thus ,
Not favouring A = (1-0.25) = 0.75
Favouring B = 0.6
Fav C= 0.5
Fav D = 0.7

Thus,Final Not Fav. A = (0.75) (0.6) (0.5) (0.7) =0.157

Thus, Fav A = 1- 0.157 = 0.85


You're overlooking the fact that 'favoring B' = 0.6 doesn't imply that 'not favoring A' is also 0.6. That's only true if the other 8 people in the second group all thought A is the correct answer. In fact, it is likely that the other 8 people's votes would have been spread across A, C, and D in some distribution that isn't 8, 0, 0.

I attempted to come up with a reasonable method for determining that distribution.

And why are you multiplying the probabilities? Let's take a very simple case:

2 choices (A and B), 2 groups with 3 people each
2 people in group 1 think A is correct
1 person in group 2 thinks B is correct

Using your method, we'd say:
not favoring A = 1/3 * 1/3 = 1/9
therefore favoring A = 8/9

not favoring B = 2/3 * 2/3 = 4/9
therefore favoring B = 5/9

Clearly, this is incorrect as the ratio 8/9 : 5/9 should be 2 : 1.
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