tinku wrote:
would like to know why the below mentioned approach is wrong? thanks
Probability = number of favorable outcomes/total number of outcomes
Total outcomes possible
1. Black,Black
2. Black,Brown
3. Brown,Black
4. Brown,Brown
favorable are 1 and 4 , so probability is 2/4 = 1/2
In order for your approach to work, it must be the case that the four possible outcomes are all
equally likely.
Since the number of brown socks is greater than the number of black socks, the outcome BROWN,BROWN is more likely than the outcome BLACK,BLACK
As such we can't use the this approach.
Here is an analogous question.
A box contains 1 red ball and 1,000,000 green balls. If a single ball is randomly drawn from the box, what is the probability that the ball is red? Of course, we know the answer my here must be 1/1,000,001
However, let's see what happens if we list all possible outcomes:
1) The selected ball is RED
2) The selected ball is GREEN
Since 1 of the 2 possible outcomes is favorable, P(select red ball) = 1/2
As you can see, if the outcomes are equally likely, this approach of listing outcomes falls apart.