# probability exam question 2e

Hi ,

I need help with question 2d and 2e from http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011mmcas2-w.pdf .

All of the chocolates produced by machine A and machine B are stored in a large bin. There is an equal number
of chocolates from each machine in the bin.
It is found that if a chocolate, produced by either machine, takes longer than 3 seconds to produce then it can easily be identified by its darker color

e. A chocolate is selected at random from the bin. It is found to have taken longer than 3 seconds to produce.
Find, correct to four decimal places, the probability that it was produced by machine A.
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Commented:
I am consulting with EE to see if we are allowed to answer an Exam related questions...

If I do not hear back from them in couple of hours I will give you the answers.
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Commented:
This is clearly an older, practice exam.
Do you really need help with part (e)?
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Commented:
How do you know it is old and not a "real-time" question ? :)
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Commented:
There is a date on the first page.....    2011
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Commented:
Well new question can be a copy of this....
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Commented:
For part (d), you can use the binomial theorem or Paschal's triangle.
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Commented:
d-glitch gave you the answer. Hopefuly you know what binomial distribution is.

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Commented:
There is not enough information given to get the answer.
Suppose that machine a produced 80% dark chocolates and machine B 20%. Then machine A most likely produced the test candy. But if the above percentages were reversed then the answer would be reversed.
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Commented:
You should be able to find the probability of producing a dark chocolate for A and B.
Assume (for the sake of simplicity) that each machine has put 32 pieces into the bin.

It would be good if you could show some work or interest.
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Commented:
>>  Hello Netminder,

I think this is more likely self study/test preparation than a academic assignment.
jagguy has several similar questions over the past few weeks.

We have been pretty careful to give help and hints rather than answers.
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Commented:
Netminder,

This test is available on the internet for individual use
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011mmcas2-w.pdf

The copyright page is here

But it is not appropriate to attach (and essentially republish) the entire 28 page exam here for these two little questions.

It would be acceptable to include the link, like I have done here.

If you can't delete the pdf attachment, you should probably delete the whole question.
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Author Commented:
This exam is an old exam made public for public use and how is this homework anyway when the answer also available?
I am helping someone with the exam and I don't understand some questions myself so i dont see how asking for such help isnt appropriate.

I am unsure how to get to the answer so that is why I am asking for help.
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Commented:
You if were able to answer question 2a, you should be able to
Find the probability that a chocolate produced on machine A takes longer than 3 seconds.
Find the probability that a chocolate produced on machine B takes longer than 3 seconds.
From this, you should be able to estimate the number of chocolates in the bin from machine A which took longer than 3 seconds to produce, and the number of chocolates in the bin from machine B which took longer than 3 seconds to produce.
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Author Commented:
ok I am not sure with 2e.
It is a given prob question I see and the workings out are simple but getting the prob
machine A =.5?
over
prob either takes > 3 sec ?
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Commented:
The question text says that Machine A has a normal prob dist with mean X=3 seconds.
Symmetry tells you that half of the output will be above the mean and half below.
The equal sign can go with either side.

If the mean were anything other than 3 seconds, you would have a more difficult problem.

If A produces 32 chocolates,  you expect 16 to be dark.
If B produces 32 chocolates, you expect ?? to be dark.
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