Probability Question (1 Viewer)

[Michaelmoo]

One hundred and fifty four blue smarties were mixed into a batch of smarties that did not contain any blue ones previously. Later, a sample of 300 smarties was taken from the batch at random. There were 55 blue smarties in this sample. Estimate how many smarties there were in the original batch before the extra blue ones were added.

 

[Affinity]

they probably want you to answer along the lines,

55/400 = 154/(154+S)
and then find S..

it's not quite the correct way to do it.. a thorough analysis would require some heavy mathematics (to approximate terms) and some computing power

 

[Michaelmoo]

they probably want you to answer along the lines,

55/400 = 154/(154+S)
and then find S..

it's not quite the correct way to do it.. a thorough analysis would require some heavy mathematics (to approximate terms) and some computing power

Yes. But it can't be too complex. It only can incorporate 2-unit knowledge. The answers is 686. I can't seem to find a relationship that allows me to get to this solution.

 

[x3.eddayyeeee]

are you sure the answer is 686?
when i worked it out, i got 966. O__O"

 

[savio23q]

Yup. 966 for shizzle.

55/400 = 154/N

cross multiply...

55N=61600

N = 1120

1120 - 154 = 966.

EDIT: This is a general math question.

 

[Affinity]

suppose we change 400 and 55 to 1... how would you answer the question now..
then you will see how ridiculous it is.

 

[Timothy.Siu]

suppose we change 400 and 55 to 1... how would you answer the question now..
then you will see how ridiculous it is

lol, good point,obviously this isn't the most accurate probability, but it just asks for a (2unit) estimate

 

[savio23q]

Drawing 1 smartie from the batch doesn't give an accurate indication as to how many the bag has in it...

The bigger the sample, the more accurate the estimation is.

If you draw 1 smartie and that smartie is blue, that means the bag has only 154 smarties in it...

The question is made so it's not ridiculous...ie. 55/400 are blue.

 

[Michaelmoo]

Yes. The answer works out now. Sorry a typo. It's 300 not 400. Yes very stupid question, was thinking of doing that but doesnt make sense, equating the two probabilities....

As savio said before, if you remove one, the probability ratio changes.

Thanks guys.

 

[untouchablecuz]

Sample 1

Let x = batch of smarties before blue are added

. ' . x + 154 = batch of smarties + blue ones

Ratio of blue to total = blue:total = 154/(x+154)

Sample 2

300 are taken from the batch of smarties with 55 blue ones.

Ratio of blue:total = 55:300 = 55/300

Theoretically, these ratios must be equal, hence

154/(x+154) = 55/300

Solving for x yields 686

 

[Timothy.Siu]

Yes. The answer works out now. Sorry a typo. It's 300 not 400. Yes very stupid question, was thinking of doing that but doesnt make sense, equating the two probabilities....

As savio said before, if you remove one, the probability ratio changes.

Thanks guys.

its just an estimate.