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### Tricky Problem On Probability

Tricky Problem On Probability - 2 August

There was a blind man. He had four socks in his drawer either black or white. He opened it and took out two socks. Now the probability that it was a pair of white socks is 1/2.

Can you find out the probability that he had taken out a pair of black socks ?

1. if the probability to have 2 white socks is 1/2 = 2/4 it means the probability to have 2 black socks is the same 1/2.

2. The probability of having 2 black socks is not complementary to the prob. of having 2 white socks.
They don't add up to 1. You can have pairs of w-b also.
4 socks can form C(4,2)=6 distinct pairs of socks.
In order that p(pair of white)=1/2 that means that 3 of these distinct pairs have to have only whites. This happens only if we have 3 whites and 1 black. Let's name 1,2,3 the white socks and 4 the black one.
Compining the white onew we have the pairs: 1-2, 1-3, 2-3. These are 3 pairs . The other 3 (the are half of the overall probability) are: 1-4, 2-4, 3-4 (one black-one white). That explains why the probability of black-black is 0. There is only one black sock.

1. 1/4

There are 3 white socks and 1 black sock (prob pair of white socks = 3/4 * 2/3 = 2/4 = 1/2)

1. srsly, if there's only one black sock how do you get a pair ?!?1/

2. You can't get a pair of black socks, since there is only 1 black and 3 white ones. That's why the p(pair of blacks)=0 (impossible event)

3. I have pulled 2 socks, random color, and after that I have one black and three white, 3/4*2/3 = 6/12 = 1/2 chance.

So what is the chance to be black? I put them back and pull agian.
So now I have 2 random, 1 black, 3 white.

A) 3 white 3 black
B) 4 white 2 black
C) 4 white 2 black
D) 5 white 1 black

This means pulling will be like:

1/4*3/6*2/5 + 2/4*2/6*1/5 + 1/4*1/6*0/5

= 1/12