2020 AMC 8 第 13 题
先试着解答 2020 AMC 8 第 13 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2020 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
13.
贾马尔的抽屉里有 只绿色袜子、 只紫色袜子和 只橙色袜子。加入一些紫色袜子后，贾马尔注意到现在随机抽到一只紫色袜子的概率是 。贾马尔加入了多少只紫色袜子？
Jamal has a drawer containing green socks, purple socks, and orange socks. After adding more purple socks, Jamal noticed that there is now a chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add?
小提示：
非紫色袜子数量保持为
The non-purple socks stay at
大提示：
若紫色占 ，非紫色就占
If purple is , non-purple is
视频讲解：
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文字解答：
设贾马尔加入 只紫色袜子，则紫色袜子共有 只。
原来共有 只袜子，加入后总数为 只。
因为之后抽到紫色袜子的概率是 ，所以
解 得
所以加入了 只袜子。
正确答案是 B。
Suppose Jamal adds purple socks. Then, there will be purple socks.
Also, since there are total socks to begin with, we have socks after adding the socks.
Since we have a chance of choosing a purple sock afterwards, we know
Solving for yields:
Therefore, socks are added.
Thus, the correct answer is B.
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