harsh.champ wrote:Tom has 5 pairs of dark Blue socks and 5 pairs of Black socks. He keeps them all in a same bag. If he picks out three socks at random what is the probability he will get a matching pair?

(A) (2 x 5C2 x 5C1) / 10C3
(B) (5C2 x 5C1) / 10C3
(C) (5C1 x 5C1) / 10C3
(D) 1
(E) None of the above.

The OA is D.

In any case u get a pair , the following possibilities could be sorted out...

Blue blue blue
black black black
blue blue black
blue black black

all gives a matching pair...
so probabaility =1

This can be solved without calculating probability.
In the first pick Tom will get either a Blue or Black. Suppose he gets Blue.
In the second pick if he gets a Blue a pair is formed. If not,
then in the third pick Blue will match with the Blue in the first pick.
Alternatively, a Black in the third pick will match with that of the second pick.
Repeat with the option if Tom gets a Black in the first pick.

This is similar to an earlier post

https://www.beatthegmat.com/stumped-on-p ... t9195.html


Melinda's lights went out. She has 3 pairs of red socks in her drawer, 2 pairs of black socks, and 5 pairs of white socks. What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color?


Similarly , this can be solved without knowledge of Probability
One needs atleast 2 picks to get a pair.
Most probably they are diff. colours, say Red and white.
In the third pick she is still unlucky and picks a black. Is she picks a Red or white she will have a pair.
NOW, in the fourth pick she will definitely get a pair.
So you need four picks to be sure you got a pair.

I have two doubts
First, she knows she has a pair in four picks, but how will she sort out the correct pair in the dark. She will still end up wearing diff. colour socks.

On a serious note does GMAT ask
Qs like this

kstv wrote:This can be solved without calculating probability.
In the first pick Tom will get either a Blue or Black. Suppose he gets Blue.
In the second pick if he gets a Blue a pair is formed. If not,
then in the third pick Blue will match with the Blue in the first pick.
Alternatively, a Black in the third pick will match with that of the second pick.
Repeat with the option if Tom gets a Black in the first pick.

This is similar to an earlier post

https://www.beatthegmat.com/stumped-on-p ... t9195.html


Melinda's lights went out. She has 3 pairs of red socks in her drawer, 2 pairs of black socks, and 5 pairs of white socks. What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color?


Similarly , this can be solved without knowledge of Probability
One needs atleast 2 picks to get a pair.
Most probably they are diff. colours, say Red and white.
In the third pick she is still unlucky and picks a black. Is she picks a Red or white she will have a pair.
NOW, in the fourth pick she will definitely get a pair.
So you need four picks to be sure you got a pair.

I have two doubts
First, she knows she has a pair in four picks, but how will she sort out the correct pair in the dark. She will still end up wearing diff. colour socks.

On a serious note does GMAT ask
Qs like this

kstv yeah you are saying right ... I meant the same thing...
I have shown the possible combination in 1st 2nd and 3rd attempt.......so its a problem of common sense like . Just by giving a single thought u can say total probability = 1...