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) 1/12B) 1/6C) 1/5D) 1/3E) 1/2

Answer 1

B.

Explanation:

let R= Red Rosebushes and W = White Rosebushes

You are expected to calculate the probability of the pattern occurrence in this order : WRRW . However, the selections must be at random .

Steps :

1. The probability that the first rosebush will be white is 2/4 (there are two white out of total 4 rosebushes) .

2. The probability that the second rosebush will be red is 2/3 (there are two reds out of total 3 rosebushes left) .

3.The probability that the third rosebush will be red is 1/2 (there are now one red out of total 2 rosebushes left).

4. Eventually, there is only one white rosebush left which means the probability is 1.

Therefore Probability(WRRW)=2/4*2/3*1/2*1=1/6.