Question

A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?

a) 1/12
b) 1/6
c) 1/5
d) 1/3
e) ½

Answer 1

Answer:   b)  $\dfrac{1}{6}$

Step-by-step explanation:

Sample space for the arrangement of red bushes :

[rrww , rwwr , wwrr , wrwr, rwrw , wrrw]

i.e. Total possible outcomes = 6

If the two rosebushes middle of the row are red , then the first and the last rosebushes must be white (wrrw).

i.e. the number of favorable outcomes for middle of the row are red =1

Now, the probability that the 2 rosebushes in the middle of the row will be the red rosebushes :

$\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{1}{6}$

Hence, the correct answer is option (b).