Probability Question - Not from a book (No official answer) : PS Archive
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# Probability Question - Not from a book (No official answer)

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Joined: 16 Mar 2010
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07 May 2010, 08:42
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Hey guys - long time lurker here and this is my first post.

My buddy at work was talking about how he plays a lottery where you pick 4 numbers and there is a drawing everyday, which got me thinking about it in terms of the gmat.

Probability of hitting the 4 numbers in order = 1 / 10^4 = 1/10,000 ?

But you can also "win the lottery" if you pick the 4 numbers correctly, not neccesarily in order.

I'm having a little trouble caluclating that number so if you all can help me understand that would be SUPER!

-Sameer
Intern
Joined: 16 Mar 2010
Posts: 42
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Kudos [?]: 8 [0], given: 39

Re: Probability Question - Not from a book (No official answer) [#permalink]

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10 May 2010, 05:34
Guys come on!!

I thought we were friends!!!!!
Senior Manager
Joined: 25 Jun 2009
Posts: 306
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Kudos [?]: 122 [0], given: 6

Re: Probability Question - Not from a book (No official answer) [#permalink]

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10 May 2010, 06:07
sameermunshi wrote:
Hey guys - long time lurker here and this is my first post.

My buddy at work was talking about how he plays a lottery where you pick 4 numbers and there is a drawing everyday, which got me thinking about it in terms of the gmat.

Probability of hitting the 4 numbers in order = 1 / 10^4 = 1/10,000 ?

But you can also "win the lottery" if you pick the 4 numbers correctly, not neccesarily in order.

I'm having a little trouble caluclating that number so if you all can help me understand that would be SUPER!

-Sameer

Okay, even though I am not an expert but let me give a shot to this one...!

So 4 numbers to choose from ..

so the probability for the 1st number on our lottery ( 4/10 ) because we have 4 numbers to choose from-- assuming we are talking about digits(0-9) here

for 2nd number it should 3/10 and similarly for 3rd number 2/10

So final probablity = $$\frac{(4 *3*2*1)}{10*10*10*10}$$

Cheers,
Intern
Joined: 16 Mar 2010
Posts: 42
Followers: 0

Kudos [?]: 8 [0], given: 39

Re: Probability Question - Not from a book (No official answer) [#permalink]

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10 May 2010, 11:12
Thanks Nitish!

So quick question:

if 4*3*2*1 /10*10*10*10 = Prob of picking 4 numbers (order doesnt matter) out of 10

what would 4*4*4*4 / 10*10*10*10 mean? ?

Anyone else have any input?

Appreciate it!!
nitishmahajan wrote:
sameermunshi wrote:
Hey guys - long time lurker here and this is my first post.

My buddy at work was talking about how he plays a lottery where you pick 4 numbers and there is a drawing everyday, which got me thinking about it in terms of the gmat.

Probability of hitting the 4 numbers in order = 1 / 10^4 = 1/10,000 ?

But you can also "win the lottery" if you pick the 4 numbers correctly, not neccesarily in order.

I'm having a little trouble caluclating that number so if you all can help me understand that would be SUPER!

-Sameer

Okay, even though I am not an expert but let me give a shot to this one...!

So 4 numbers to choose from ..

so the probability for the 1st number on our lottery ( 4/10 ) because we have 4 numbers to choose from-- assuming we are talking about digits(0-9) here

for 2nd number it should 3/10 and similarly for 3rd number 2/10

So final probablity = $$\frac{(4 *3*2*1)}{10*10*10*10}$$

Cheers,
Senior Manager
Joined: 25 Jun 2009
Posts: 306
Followers: 2

Kudos [?]: 122 [0], given: 6

Re: Probability Question - Not from a book (No official answer) [#permalink]

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10 May 2010, 11:27
sameermunshi wrote:
Thanks Nitish!

So quick question:

if 4*3*2*1 /10*10*10*10 = Prob of picking 4 numbers (order doesnt matter) out of 10

what would 4*4*4*4 / 10*10*10*10 mean? ?

Anyone else have any input?

Appreciate it!!
nitishmahajan wrote:
sameermunshi wrote:
Hey guys - long time lurker here and this is my first post.

My buddy at work was talking about how he plays a lottery where you pick 4 numbers and there is a drawing everyday, which got me thinking about it in terms of the gmat.

Probability of hitting the 4 numbers in order = 1 / 10^4 = 1/10,000 ?

But you can also "win the lottery" if you pick the 4 numbers correctly, not neccesarily in order.

I'm having a little trouble caluclating that number so if you all can help me understand that would be SUPER!

-Sameer

Okay, even though I am not an expert but let me give a shot to this one...!

So 4 numbers to choose from ..

so the probability for the 1st number on our lottery ( 4/10 ) because we have 4 numbers to choose from-- assuming we are talking about digits(0-9) here

for 2nd number it should 3/10 and similarly for 3rd number 2/10

So final probablity = $$\frac{(4 *3*2*1)}{10*10*10*10}$$

Cheers,

Well, Say for e.g the case would have been that we need to pick 4 numbers in any order and at any place holder.

For e.g winning lottery number would have been 4678 and so the condition would have been something like 4 numbers
any order like 4468 or may be even 6777 ( I mean to say any number can fit any where even with repetition then

\frac{4*4*4*4}{10*10*10*10}

Would have fit the bill...!

Cheers
Senior Manager
Joined: 21 Jul 2009
Posts: 366
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
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Re: Probability Question - Not from a book (No official answer) [#permalink]

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10 May 2010, 12:18
Is my understanding wrong??

You have 10 digits from 0 to 9 inclusive. You are selecting one number from the 10 for every place, thus you select 4 times to get a four digit number - (10C1)^4 = 10 * 10 * 10 * 10 = 10000.

All possible 4 digit numbers - 9 * 10 * 10 * 10 = 9000 (have to give up 0 for the first spot).

Probability of choosing a 4 digit number from the entire lot = 10000/9000 = 10/9 > 1.

Is this even possible? what am I doing wrong with the question??
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Re: Probability Question - Not from a book (No official answer)   [#permalink] 10 May 2010, 12:18
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