Hi Megha,
The math that's required to answer this question can actually be done in a couple of different ways, depending on how you "see" probability questions.
We're given 2 red rosebushes (R1 and R2) and two white rosebushes (W1 and W2). We're told to put these 4 rosebushes in a row; the question asks for the probability that the "middle two" rosebushes are both red.
Probability is defined as…
(# of ways that you want)/(# of ways that are possible)
The # of ways that are possible = (4)(3)(2)(1) = 24 possible ways to arrange the 4 bushes.
The specific ways that we want have to fit the following pattern:
W-R-R-W
The first bush must be white; there are 2 whites
The second bush must be red; there are 2 reds
The third bush must be red, but after placing the first red bush, there's just 1 red left
The fourth bush must be white, but after placing the first white bush, there's just 1 white left
= (2)(2)(1)(1) = 4
4 ways that fit what we want
24 ways that are possible
4/24 = 1/6
Final Answer:
GMAT assassins aren't born, they're made,
Rich