Last Question of the Paper (inc soln.) (1 Viewer)

[mirror-match]

So what is everyone's thoughts on the last question with Juan?

This was my solution, all decimals are to 2 d.p.:

-First list the sample space from rolling 1,1 to 6,6

-Ultimately there ends up being 21 unique possibilities out of 36
(6 for the ones, 5 for twos, 4 for threes, 3 for fours, 2 for fives and one for 6's)

-Convert the chance for attaining a specific difference into a percentage
which just so happens to be for differences 6/21 for diff of 0, 5/21 for diff of 1 and so on down to 1/21 for diff of 5.

-P(diff of 0) = 6/21 * 100 = 28.57%
-Multiply 18 (the number of rolls he did) by this percentage
-18 * 28.57% = 5.14
- round to nearest number hence, 5, this means 5/18 times a difference of 0 will come up

-P(diff of 1) = 5/21 * 100 = 23.80%
-18 * 23.80% = 4.24
-hence, 4

-P(diff of 2) = 4/21 * 100 = 19.05%
-18 * 19.05% = 3.43
-hence, 3

-P(diff of 3) = 3/21 * 100 = 14.29%
-18 * 14.29% = 2.57
-hence, 3

-P(diff of 4) = 2/21 * 100 = 9.52%
-18 * 9.52% = 1.71
-hence, 2

-P(diff of 5) = 1/21 * 100 = 4.76%
-18 * 4.76% = 0.86
-hence, 1

.'. Your theoretical probability, if plotted in a table would look something like this:

Theoretical probability
Difference | Frequency
----------------------------

0 | 5
1 | 4
2 | 3
3 | 3
4 | 2
5 | 1
​

this differs little from the second table, whose only difference is an extra 1 in the difference of 5 instead of in the difference of 0;

Table 2 in exam
Difference | Frequency
----------------------------

0 | 4
1 | 4
2 | 3
3 | 3
4 | 2
5 | 2
​

Hence you can see that, the second table was, infact, a more accurate representation of the theoretical probability, as opposed to the other one which I cant remember off the top of my head. I hope thats right at least.

Where:
* = Multiply
/ = Divide

How'd you guys go?

 

[hazza9]

I had the same idea but i think you may have got some probablities mixed up

This is what i did

View attachment 19660

If you can't read it jst zoom in soz

What u think?

 

[mirror-match]

yeah i see what you did, you used all 36 different combinations as opposed to the 21 unique ones that i did, that's the only difference. But rolling 2,1 is the same as 1,2 in this case because if they were considered to be seperate cases then there would be differences of -1, -2, -3, -4, -5 wouldn't there?

 

[hazza9]

Nah i dnt think so because what your theoretic probability says is that it is more likely to get a difference of 0, when really it is much more likely to get a difference of 1.

You have to include all the sample space. You wouldn't end up wth negatives because its the difference between them, not dice 1 minus dice 2 or vica-versa.

I'm not 100% sure on this but it makes more sense + u get whole number answers

 

[mirror-match]

Mmmm, I see where your coming from, and it makes sense too, I might have made a mistake, but thats just 1 mark :3

 

[jo-di-e]

the last question really got me lol i didnt have a clue what to do, we didnt do it in class i dont think...:mad1:

 

[mirror-match]

Yeah, thats the thing with question 28, in all the general maths papers, its an application of something you learnt, but in a way you didn't learn the concept to be used. In the 2008 paper it was with simpson's rule so eh.. whaddya gonna do... its over now anyways

 

[sadcase]

I did not have time answering it but i did put that he was correct. can i get 1 mark for that?

 

[mirror-match]

I'd assume so, because 1 mark goes to sample space, probably 2 to proving that he was right, and the 4th in stating if he was right or not. Because thats what the question asked.

 

[sadcase]

I hope so
lol...
I just took a wild guess and said he was correct. I will be happy with just 1 mark for that question
lol

 

[uart]

No doubt the correct answer was "Juan is correct, experiment 2 was closer to theoretical"

It seems that most people who managed to get the theoretical probabilities correct could also get the right answer "by inspection" but I'm just wondering if anyone tried anything quantitative? Something like finding the mean square error or the mean absolute deviation for example. Did anyone try that?