표와 제한된 집합에서의 확률
SAT 주제 16 3:36 영어 내레이션 · 영어 + 중국어 자막 burned-in
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전사본
Conditional probability restricts the denominator.
条件概率限制了分母。
Of 40 club members, 12 cycle; 8 of those cyclists wear a helmet.
在40名俱乐部成员中，有12人骑自行车；其中8名骑行者戴头盔。
P of H given C equals n of H intersection C divided by n of C equals 8 over 12 which is 2 over 3.
P(H|C) = n(H∩C)/n(C) = 8/12 = 2/3。
The group is cyclists, so 40 is not this denominator.
群体是骑行者，所以40不是这个分母。
Each task gives its own data.
每个任务都有各自的数据。
Do not copy the worked example’s numbers.
请勿照搬示例中的数值。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
Tea drinkers total 21 of 50, so the probability of T is 21 over 50.
喝茶的人一共是五十人中的二十一人，所以 P(T) 等于五十分之二十一。
Within cyclists, the probability of T given C is 12 over 20, or three fifths.
在骑车的人中，P(T|C) 等于二十分之十二，即五分之三。
Within tea drinkers, the probability of C given T is 12 over 21, or four sevenths.
在喝茶的人中，P(C|T) 等于二十一分之十二，即七分之四。
These different denominators make the conditional probabilities unequal.
分母不同，所以这两个条件概率不相等。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
They are not independent, because the probability of T given C, three fifths, is not equal to the probability of T, 21 over 50.
它们不独立，因为 P(T|C) 等于五分之三，不等于 P(T)，即五十分之二十一。
They are not disjoint, because 12 respondents do both; the probability of T and C is 12 over 50, which is greater than 0.
它们也不互斥，因为有十二位受访者两样都做；P(T 且 C) 等于五十分之十二，大于零。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
Use inclusion-exclusion.
使用容斥原理。
The probability of W or T is 30 plus 21 minus 9, over 50, which is 42 over 50, or 21 over 25.
P(W 或 T) 等于三十加二十一减九，再除以五十，即五十分之四十二，也就是二十五分之二十一。
The 9 tea-drinking walkers must not be counted twice.
九位既步行又喝茶的人不能被重复计算。
Equivalently, exclude the 8 cyclists who do not drink tea.
等价地，也可以排除八位不喝茶的骑车者。
Return to the task and explain why the method fits.
回到该任务，并解释为何此方法适用。
Original practice does not predict an official score.
原始练习无法预测正式成绩。
Complete required live or recorded evidence separately.
请单独完成所需的现场或录制证据。
Pause and test yourself. Cover the worked answer, rebuild the answer to the last example in your own words, and name one condition that would change it before you check.
暂停一下，自我检测：遮住示范答案，用自己的话重做最后一个例子的答案，并在核对之前说出一个会改变结论的条件。