下表显示了不同颜色容器中夹子的数量。

1. Express the ratio of the number of clips in white containers to blue containers

Ratio of clips in white containers to blue containers = $3 : 2$
Let the number of clips in white containers be $3u$ and the number of clips in blue containers be $2u$.

2. Find the number of white and blue containers in terms of units

Number of clips per white container = $30$
Number of white containers = $\frac{3u}{30} = \frac{u}{10}$

Number of clips per blue container = $50$
Number of blue containers = $\frac{2u}{50} = \frac{u}{25}$

3. Calculate the fraction of blue containers out of the total containers

Total number of containers = $\frac{u}{10} + \frac{u}{25} = \frac{5u}{50} + \frac{2u}{50} = \frac{7u}{50}$

Fraction of blue containers = $\frac{\frac{u}{25}}{\frac{7u}{50}} = \frac{u}{25} \times \frac{50}{7u} = \frac{2}{7}$