一个袋子里装有 4 枚黑色硬币、7 枚红色硬币和 11 枚白色硬币。从袋子里随机连续抽取两枚硬币（不放回）。

1. Find the probability that the second coin drawn is white

Total number of coins $=4+7+11=22$.

There are $11$ white coins, so
$P(\text{white on second draw})=\frac{11}{22}=\frac{1}{2}.$

1. Find the new total number of coins after adding yellow coins

Originally, total number of coins
$=4+7+11=22$.

After adding $x$ yellow coins, total number of coins
$=22+x$.

2. Form the probability of drawing two black coins without replacement

There are still $4$ black coins.

Probability of first black coin $=\dfrac{4}{22+x}$.

After one black coin is drawn, there are $3$ black coins left out of $21+x$ coins.

So,
$\frac{4}{22+x}\times \frac{3}{21+x}=\frac{1}{50}.$

3. Solve the equation for $x$

$\frac{12}{(22+x)(21+x)}=\frac{1}{50}$
$(22+x)(21+x)=600$

Since $24\times25=600$,
$21+x=24 \quad \text{and} \quad 22+x=25.$

Hence,
$x=3.$