# Google offers Adwords deals - but you can't trust their numbers

Google's Adwords platform has always been something of a mystery, to put it mildly - the only certainty about it is that it makes a lot of money for Google - but nobody has caught it out using numbers which are definitely, verifiably untrue. Until now. Simples An eagle-eyed Reg reader has broken this long run of success. …

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#### More marbles

The riddle is rather trivial, so I wonder how they managed to screw the answer... or lost the count of their marbles in this particular case.

The 1st time I read it it appeared to me blue and green marbles also had 3/5 odds to be picked and that would have made the bag sort of magic or voodoo magic. The latter would explain adwords deals nicely.

#### Re: More marbles

I think it's a simple clerical error. The answer is (3*3)/(14*15), or 9/210. This simplifies to 3/70, but I think they've just simplified the denominator.

#### Re: More marbles

@Arbee, or they are color blind and mistook red for green. :)

#### Re: More marbles

An unforgivable mistake.

#### Insufficient data in the question...

I sort of assumed that the marble was returned to the bag after selection, giving the slightly lower rate of (3*3)/(15*15) = 9/225 = 1/25

Doh.

#### Re: Insufficient data in the question...

Though the chance of pulling a green marble on the second draw should be lower. You have already pulled out a blue one, so your luck favours blue.

Well, that is how many play roulette.

#### Re: Insufficient data in the question...

I think that if you're Google you look in the bag and pick the colour you want. That would explain a lot about how ads work on Google:-)

#### Re: Insufficient data in the question...

"I sort of assumed that the marble was returned to the bag after selection"

I did the same.

#### A bag contains fifteen marbles.

Unless you live at Mountain View.

In which case, you've probably lost a few.

Is it just me or could the excerpt:

'The probability of choosing a red marble from the bag is 3/5. There is an equal probability of choosing either a blue or green marble'.

be read to mean that there is as equal a chance of getting a blue/green marble as a red one? this would mean that the actual probability would be:

9/15 * 9/14 = 81/210

Fail, just in case Stephen Fry comes in here and puts me right on my grammar...

#### That would be a very special bag

Which would allow you to have a red marble with probability 3/5, a blue marble with probability 3/5, and a green marble with probability 3/5, for a total of 9/5. Which would mean that almost every time you choose a marble, you end up choosing two at the same time!

I mentioned that was the way I read it first but it required the voodoo bag so I discounted the option.

#### Re: That would be a very special bag

Exactly, which is why this is an epic combination of 'question' and 'answer' fail by Google.

#### I hate questions like that...

...precisely because they never state whether each pick is replaced before the next one. But whatever the quizmaster was thinking is "right" even though a crucial fact was kept sekrit.

(Still not figured out how to get an Addsense website linked to youtube, as both send you to links on the other site THAT LINK BACK!)

#### Assumptions

The probability of picking a red marble is 3/5 and there are 15 marbles, therefore 9 of the marbles must be red?

How very presumptuous of people to assume that Google are wrong.

Could the marbles be different sizes/weights/temperatures?

Could the contents of the bag be visible so people’s preferences to colour may affect the results?

Could not picking a marble be an option?

This is clearly Google’s way of saying that adwords is a black box and you just need to trust them at their word.

#### Google's mistake was transcription, not maths

It looks like this problem was copied from here:

http://www.mathplayground.com/MTV/mathtv11.html

In this example the question is identical EXCEPT at the very end its uses a red marble instead of a green one. The result is the 9/70 as per Google's answer page.

So they didn't plagiarise the question properly....

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