There are 4 cars. Each of them are either black or white.

Question

There are 4 cars. Each of them are either black or white. What is the probability that there are two black and two white cars?

conocieur · Answer

let's call x: the event of getting a white card
then the Probability of getting two whites and two blacks out of four cards is the same as X=2

then use binomial

4c2 * (1/2)^2 * (1/2)^2

6*(1/16)

6/16 so the answer is 3/8

ipc302 · Answer

4 cars either black or white

lets see what are the possible combinations possible

WWWW
WWWB
WWBB
WBBB
BBBB

so total 5 combination possible and we need one

so the probablity should be 1/5 ...

please let us know the OA . I hope i didnt make any basic blunder here . :roll:

ywilfred · Answer

4 cars so we can have WWWW, BBBB, WWBB, WWWB, BBBW combinations.

P = 1/5

razrulz · Answer

wwww
wwwb
wwbb
wbbb
bbbb 

 1/5 is the answer

joemama142000 · Answer

the oa is 3/8.

there may be a mistake in the q. however. 

conoceiur can you expalin your method? I have no idea how to do binomial. thanks in advance.

believe2 · Answer

conocieur has a slick method.

Here is a quick & dirty method:
I think we can use this method here because the prob of having a white car=prob of having a black car

No. of ways of getting 2 W & 2 B = 4c2 = 6

All possible ways of getting white (or black) cars= 
4c0 + 4c1 + 4c2 + 4c3 + 4c4
=16

so the prob of getting 2 white = 6/16=3/8

conocieur · Answer

there are 4 events _ _ _ _ that can be black or white with a 50% chance

therefore p= 0.5 (1-p)=.5 and n=4 k=succesful event
p^k * (1-p)^n-k and it happens in nCk combinations

therefore 4c2 * (.5)^2 * (.5)^2

I hope that explains my approach, but anyway you can find it in any introduction to probability textbook

There are 4 cars. Each of them are either black or white.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards