跟读练习: Grade 11: Conditional Probability - 通过YouTube学习英语口语
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probability is just about figuring out how likely something is to happen if you flip a coin there are
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probability is just about figuring out how likely something is to happen if you flip a coin there are
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two possible outcomes heads or tails each one has a one out of two chance so the probability of getting
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heads is one divided by two if you roll a dice and want a three you have one chance out
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of six so probability is always a number between zero and one where zero means impossible and
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one means it's guaranteed to happen this is a simple probability now comes the fun part called
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conditional probability imagine you have a bag with five red balls and five blue balls you close your eyes and
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pick one ball and it turns out to be red what was the probability of finding this red ball yes it's simple
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answer is five out of ten or one half because we have five red balls and five blue balls which means a total of ten balls now without putting it back you pick another ball
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what's the probability this next ball is also red it's no longer five out of ten because one red ball is already gone.
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Now there are four red balls and five blue balls left, which means nine balls in total.
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So your second pick depends on the first.
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This is a conditional probability where what happens next depends on what already happened.
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So in short, conditional probability is just regular probability.
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But you already know something, and you use that knowledge to update your chances.
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Awesome!
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So now that we understand what conditional probability means, let's explore the formula behind it.
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Picture a Venn diagram.
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Imagine two overlapping circles, one for event A, which tells that even A has occurred, and one for event B, which tells that even B has occurred.
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The overlapping area, or this region, represents the cases where both A and B happen together, and we call it as event A intersection with event B.
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Suppose you want find the chance of some event A happening, but you already know that another event B has happened.
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This means we are focusing only on the B circle, and inside that circle the overlapping area is the part that also has A.
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So the probability of A given B is just asking, out of everything in the B circle, how much is also in A?
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That's exactly what conditional probability means.
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Therefore, the formula will now be simple.
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The conditional probability of A given B, which we represent like this, is equal to the probability of both A and B happening together, divided by the probability of just B happening, and that's it.
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Now let's look at a super simple example.
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Imagine there are 100 students in a school.
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Out of them, 50 students play football.
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and out of those 50, 30 also play basketball.
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So, we know that 30 students play both football and basketball.
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Now, suppose someone says, Hey, I picked a student and I already know that the student plays football.
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So, what are the chances that the same student also plays basketball?
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Since we already know this student plays football, we're no longer thinking about all 100 students, and we're only focused on the 50 who play football.
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And out of those 50, 30 also play basketball.
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So the chance that this student plays basketball, given that they play football, is simply 30 divided by 50, which is 3 divided by 5, or 60%.
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So the answer is 60%.
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That's a clear example of conditional probability, where we use what we already know to figure out the chance of something else.
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Now let's look at how this fits into the actual formula.
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Let's call the event of playing basketball as event A and the event of playing football as event B.
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So the probability of both events A and B happening together, that is, a student who plays both basketball and football or P of A intersection B is 30 out of 100.
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That's the overlapping part in the Venn diagram.
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Now the probability of just event B, that is a student playing football, is 50 out of 100.
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So the conditional probability of A given B is simply the probability of both A and B divided by the probability of B.
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That's 30 divided 100 whole divided by 50 over 100, which gives us the same 3 out of 5 or 60 percent.
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This is how the formula works behind the scenes.
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So good!
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Thank you.
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在学习英语的过程中，口语交流是一项至关重要的技能。通过观看这个有关条件概率的视频，您不仅能理解复杂的数学概念，还能提高您的英语口语能力。视频中的逐步讲解使得每一个概念都变得生动有趣，并且可以帮助学习者在实际情境中运用相关表达。这种口语练习不仅适合日常对话，也非常适合进行雅思口语练习，提升您的表达自信心。
语法与句型分析
- 条件概率：视频中提到“如果发生事件 A，那事件 B 的概率是…”这种句型，强调了条件关系。这种表达方式在说英语时非常重要，尤其是当您想解释一个结果是如何依赖于先前情况时。
- 总数与子集：例如，“在这 100 名学生中，有 50 名学生踢足球”，使用这种结构可以清晰地展示某一总体情况以及其子集，有助于提高您描述数据的能力。
- 分母与分子：用于解释条件概率公式时，提及“分子是两个事件同时发生的概率，分母是单一事件发生的概率”，这种逻辑性强的表达，能够帮助学生更好地理解相关概念。
常见发音陷阱
在视频中，有几个词汇可能会给英语学习者带来发音上的困扰。例如，“probability”和“conditional”这两个词的发音较为复杂，尤其是重音和音节划分。此外，注意句子中的连读现象，学习如何自然地连接词语将有助于提高您在实际交流中的流利度。通过模仿与
shadow speech，您可以有效地提高英语发音，掌握更地道的表达方式。
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跟读法 (Shadowing) 是一种有科学依据的语言学习技巧，最初开发用于专业口译员的培训，并由多语言者Alexander Arguelles博士普及。这个方法简单而强大：您在听英语母语原声的同时立即大声重复——就像是一个延迟1-2秒紧跟说话者的影子。与被动听力或语法练习不同，跟读法强迫您的大脑和口腔肌肉同时处理并模仿真实的讲话模式。研究表明它能显着提高发音准确性，语调，节奏，连读，听力理解和口语流利度——使其成为雅思口语备考和真实英语交流最有效的方法之一。