Probability or ratio question

Question

There are some counters in a box . Each counter is blue or red or green. There are twice as many blue counters as red counters and three times as many green counters as blue counters. One counter is picked at random from the box. Work out the probability this counter is green.

Answer 1

Let the number of red counters be n.

Then #(blue counters) = 2n, and #(green) = 3*(#blue) = 3*(2n) = 6n.

The probability of a randomly picked counter bein green = (how many green counters there are) / (how many counters there are) = 6n / (n + 2n + 6n) = 6n / 9n = 2/3.