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Probability question

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by sapuna » Thu Sep 24, 2015 12:12 pm
The likehood that A happens 10 times in a row is 0,7 (those 10 times are independenant of one another). What is the chance that it will happen not fewer than 4-x times?
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by [email protected] » Thu Sep 24, 2015 6:36 pm
Hi sapuna,

What is the source of this question? I ask because it isn't written in proper 'GMAT style", the prompt does not include the 5 answer choices (which could be quite helpful, considering the complexity of the prompt) and the number "0,7" is unclear (is it meant to be 70% or .7%?). Is this from a GMAT book or a 'math' book?

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by Matt@VeritasPrep » Fri Sep 25, 2015 12:04 am
Suppose the probability that A happens = p.

We have p¹� = .7, so p = the tenth root of .7.

I think the question then asks "what is the probability that not-A happens before A has happened at least 4 - x times". (It's so poorly worded that I'm having a hard time interpreting it, though.) This would be the sum of the following probabilities:

not-A happens the first time
A happens the first time, then not-A happens the second time
A happens the first TWO times, then not-A happens the third time,
...,
A happens the first 3 - x times, then not-A happens the (4-x)th time

This sum is tough to write without LaTeX formatting, but it's something like

(1 - (tenth root of .7)) + (1 - (tenth root of .7))(tenth root of .7) + (1 - (tenth root of .7))(tenth root of 7)² + ... + (1 - (tenth root of .7))(tenth root of 7)³�ˣ

But one issue here is that (4 - x) must be ≥ 0, so 4 ≥ x, making this sum a rather pointless thing to represent in terms of x.

Strange question.
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by sapuna » Fri Sep 25, 2015 2:13 am
Nah, the question is the same. My girl friend is taking Russian GMAT classes so I did my best to translate it correctly. Her teacher didn`t give her the possible answers.

The probability of A happening ten times in a row is 70 % ( or 0,7 as I wrote). Those 10 attempts are not connected with one another. An example of this is when you pick balls out of a bag and you return the balls after each attempt so the probability always stays the same. The exact question is this:

What is the probability that A will happen not fewer ( either = or > ) than 4-x times.
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by Matt@VeritasPrep » Fri Sep 25, 2015 10:47 am
sapuna wrote:Nah, the question is the same. My girl friend is taking Russian GMAT classes so I did my best to translate it correctly. Her teacher didn`t give her the possible answers.

The probability of A happening ten times in a row is 70 % ( or 0,7 as I wrote). Those 10 attempts are not connected with one another. An example of this is when you pick balls out of a bag and you return the balls after each attempt so the probability always stays the same. The exact question is this:

What is the probability that A will happen not fewer ( either = or > ) than 4-x times.
Tell her to find a new class or a new instructor! The question isn't at all like a GMAT question; it sounds more like a (poorly conceived) Probability 201 question that the instructor him/herself thought was interesting. Asking for (4 - x) is particularly pointless, since your only x values are 0, 1, 2, 3, and 4, so a closed form equation seems irrelevant.

One of the (many) issues with this problem is that you need to know how many times A or not-A can happen at all, and whether A needs to happen (4 - x) times in a row, or simply (4 - x) times out of whatever sample you're using. I made some assumptions trying to resolve this above, but really you can't know without the prompt stipulating it.
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