依數學傳播 28 期卷2 之公式，為
\(\displaystyle -2+\frac{3}{3+5}+\frac{4}{4+5}+\frac{6}{6+5}+5\cdot(\frac{1}{12}+\frac{1}{14}+\frac{1}{15}-\frac{1}{1 8})=\frac{359}{1848} \)。
個人的做法分類和條件機率，依取完的順序有，以下六種情形，機率分別為
白紅黃黑：\(\displaystyle \frac{6}{18}\cdot\frac{4}{12}\cdot\frac{3}{8} \)；白紅黑黃：\(\displaystyle \frac{4}{18}\cdot\frac{6} {14}\cdot\frac{3}{8} \)；白黃紅黑：\(\displaystyle \frac{6}{18}\cdot\frac{3}{12}\cdot\frac{4}{9} \)
白黃黑紅：\(\displaystyle \frac{3}{18}\cdot\frac{6}{15}\cdot\frac{4}{9} \)；白黑紅黃：\(\displaystyle \frac{4}{18}\cdot\frac{3} {14}\cdot\frac{6}{11} \)；白黑黃紅：\(\displaystyle \frac{3}{18}\cdot\frac{4}{15}\cdot\frac{6}{11} \)
故白球先取完之機率為 \(\displaystyle \frac{6}{18}\cdot\frac{4}{12}\cdot\frac{3}{8}+\frac{4}{18}\cdot\frac{6}{14}\cdot\frac{3}{8}+\frac{6}{18}\cdot\frac{3}{12}\cdot\frac{4}{9}+\frac{3}{18}\cdot\frac{6}{15}\cdot\frac{4}{9}+\frac{4}{18}\cdot\frac{3}{14}\cdot\frac{6}{11}+\frac{3}{18}\cdot\frac{4}{15}\cdot\frac{6}{11}=\frac{359}{1848} \)
