简的盒子里装有 8 支红笔、4 支蓝笔和 6 支绿笔。 她随机取出两支笔，一次取一支，不放回。 下面的树状图给出了第一支笔和第二支笔的概率。

1. Find the probability that the first pen is green.

There are $6$ green pens out of $18$ pens.

$p=\frac{6}{18}=\frac{1}{3}$

2. Find the probability that the second pen is blue, given that the first pen was blue.

If the first pen was blue, there are $3$ blue pens left out of $17$ pens.

$q=\frac{3}{17}$

1. Calculate the probability of getting one blue pen and one green pen in either order.

One blue and one green can happen in two ways:

$P(B\text{ then }G)+P(G\text{ then }B)$

$=\frac{2}{9}\times\frac{6}{17}+\frac{1}{3}\times\frac{4}{17}$

$=\frac{12}{153}+\frac{4}{51}$

$=\frac{12}{153}+\frac{12}{153}=\frac{24}{153}=\frac{8}{51}$

1. List the possible ordered outcomes where the two pens are of different colours.

Different colours can occur as:

$RB, RG, BR, BG, GR, GB$

2. Calculate and add the probabilities of all different-colour outcomes.

3. Simplify the probability.

$\frac{104}{153}=\frac{34}{51}$