# Numeric Aptitude Test

### #1

Posted 09 November 2006 - 04:48 PM

Here is an example:

A bag contains 12 green tokens and 8 yellow tokens. If a token is taken out at random and not replaced, then another token is taken out-

What is the probability that both tokens are green?

And if two tokens are taken out together at random, what is the probability that both tokens are green?

How to solve such difficult maths problems?

### #2

Posted 09 November 2006 - 06:26 PM

the second part is easy: "if you take them together":

the probability is: (12/20)*(11/19)

There's a forumla which should solve oyur problem no matter what the conditions...if you take the tokkens out together.

that's it in forumula.

a - category I objects.

b - category II objects

you take n (n<=a+b ) objects together, what is the probability that x are the I category and y the II category.

The probability is (see picture):

so you understand

C followed by the letters means combinations of that givven number-lower part takken each upper number (i'm translating mot-a-mot from romanian), which can be calculated by the following formula: C k->up, n->down: n!/(k!*(n-k)!)

As for the first part, it's a bit more difficult since the second event is conditioned by the first, i have to think about that a little longer (and force some things back into my head), but i'll let you know in the near future...

### #3

Posted 09 November 2006 - 06:46 PM

If the first question becomes:

A bag contains 12 green tokens and 8 yellow tokens. If a token is taken out at random and REPLACED, then another token is taken out-

What is the probability that both tokens are green?

Then is it the same as the above-mentioned Question 2?

The probability is: (12/20)*(11/19) ?

Forget about the first question in Post 1. It is too difficult for such kind of tests, as there is great time pressure. In fact, I asked the first question myself as I was curious to know how to solve that problem. I took the second question from a test paper, the first question was asked by me myself.

### #4

Posted 09 November 2006 - 06:52 PM

now oyu have a more possibilities depending on the tokken that's put back (yellow or green) - that's even more difficult.

### #5

Posted 17 January 2007 - 08:31 AM

**~^Whizard^~**

### #6

Posted 17 January 2007 - 04:00 PM

http://www.mathgoodi...ent_events.html

You may find experiment four of use

Thanks, although it's a bit late.

Last Saturday, I took a written test for ANZ (Australia & New Zealand Banking Group) and I finished only about 60% of the numerical questions. To makes things worse, HSBC, Hang Seng Bank and ANZ used the same test papers. So these questions were very familiar for those who had taken the written test with HSBC and/or Hang Seng this year.

Anyway, the site you referred to is very helpful. I will benefit from it in my future written tests.

### #7

Posted 17 January 2007 - 04:28 PM

Solution:

P(A) - probability that 1-st taken token is green

P(B ) - probability that 2-st taken token is green

P(AB ) = P(A)*P(A|B )

P(A) = 12/20

P(A|B ) = 11/19

So, P(AB ) = 12/20*11/19 = 0.347

If two tokens are taken out together at random:

P(AB) = P(A)^2

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### #8

Posted 17 January 2007 - 04:58 PM

I'm sorry! I've just found your thread - I know this sum! I've passed exam in probability theory )))

Solution:

P(A) - probability that 1-st taken token is green

P(B ) - probability that 2-st taken token is green

P(AB ) = P(A)*P(A|B )

P(A) = 12/20

P(A|B ) = 11/19

So, P(AB ) = 12/20*11/19 = 0.347

If two tokens are taken out together at random:

P(AB) = P(A)^2

Thanks, now I think that sometimes learning maths is fun, with all kinds of interesting models.

### #9

Posted 17 January 2007 - 06:47 PM

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### #10

Posted 23 January 2007 - 12:01 AM

Michael

### #11

Posted 23 January 2007 - 04:03 PM

### #12

Posted 23 January 2007 - 04:53 PM

I was learning limits at the begining of the first year education in Finance Academy!

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### #13

Posted 23 January 2007 - 04:57 PM

### #14

Posted 23 January 2007 - 05:11 PM

Differential equation - hardcore!

But it is very interesting!

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### #15

Posted 15 February 2007 - 07:47 AM

**~^Whizard^~**