跟讀練習: Grade 11: Conditional Probability - 通過影片學習英語口語

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probability is just about figuring out how likely something is to happen if you flip a coin there are

two possible outcomes heads or tails each one has a one out of two chance so the probability of getting

heads is one divided by two if you roll a dice and want a three you have one chance out

of six so probability is always a number between zero and one where zero means impossible and

one means it's guaranteed to happen this is a simple probability now comes the fun part called

conditional probability imagine you have a bag with five red balls and five blue balls you close your eyes and

pick one ball and it turns out to be red what was the probability of finding this red ball yes it's simple

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

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.

Now there are four red balls and five blue balls left, which means nine balls in total.

So your second pick depends on the first.

This is a conditional probability where what happens next depends on what already happened.

So in short, conditional probability is just regular probability.

But you already know something, and you use that knowledge to update your chances.

Awesome!

So now that we understand what conditional probability means, let's explore the formula behind it.

Picture a Venn diagram.

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.

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.

Suppose you want find the chance of some event A happening, but you already know that another event B has happened.

This means we are focusing only on the B circle, and inside that circle the overlapping area is the part that also has A.

So the probability of A given B is just asking, out of everything in the B circle, how much is also in A?

That's exactly what conditional probability means.

Therefore, the formula will now be simple.

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.

Now let's look at a super simple example.

Imagine there are 100 students in a school.

Out of them, 50 students play football.

and out of those 50, 30 also play basketball.

So, we know that 30 students play both football and basketball.

Now, suppose someone says, Hey, I picked a student and I already know that the student plays football.

So, what are the chances that the same student also plays basketball?

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.

And out of those 50, 30 also play basketball.

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%.

So the answer is 60%.

That's a clear example of conditional probability, where we use what we already know to figure out the chance of something else.

Now let's look at how this fits into the actual formula.

Let's call the event of playing basketball as event A and the event of playing football as event B.

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.

That's the overlapping part in the Venn diagram.

Now the probability of just event B, that is a student playing football, is 50 out of 100.

So the conditional probability of A given B is simply the probability of both A and B divided by the probability of B.

That's 30 divided 100 whole divided by 50 over 100, which gives us the same 3 out of 5 or 60 percent.

This is how the formula works behind the scenes.

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為什麼要通過這個影片練習口語？

在學習英語的過程中，口語交流是一項至關重要的技能。通過觀看這個有關條件機率的影片，您不僅能理解複雜的數學概念，還能提高您的英語口語能力。影片中的逐步講解使得每一個概念都變得生動有趣，並且可以幫助學習者在實際情境中運用相關表達。這種口語練習不僅適合日常對話，也非常適合進行雅思口語練習，提升您的表達自信心。

語法與句型分析

條件機率：影片中提到“如果發生事件 A，那事件 B 的機率是…”這種句型，強調了條件關係。這種表達方式在說英語時非常重要，尤其是當您想解釋一個結果是如何依賴於先前情況時。
總數與子集：例如，“在這 100 名學生中，有 50 名學生踢足球”，使用這種結構可以清晰地展示某一總體情況以及其子集，有助於提高您描述資料的能力。
分母與分子：用於解釋條件機率公式時，提及“分子是兩個事件同時發生的機率，分母是單一事件發生的機率”，這種邏輯性強的表達，能夠幫助學生更好地理解相關概念。

常見發音陷阱

在影片中，有幾個詞彙可能會給英語學習者帶來發音上的困擾。例如，“probability”和“conditional”這兩個詞的發音較為複雜，尤其是重音和音節劃分。此外，注意句子中的連讀現象，學習如何自然地連線詞語將有助於提高您在實際交流中的流利度。通過模仿與
shadow speech，您可以有效地提高英語發音，掌握更地道的表達方式。

影片中的語法

說話人最常用的結構，並附上影片中的原話：

結構	影片中的用法
定語從句 who / which + 從句 — 補充說明人或事物	balls which means · left, which means · student who plays
現在完成時 have/has + 過去分詞 — 過去發生但與現在仍有關聯的事	has occurred · has happened

什麼是跟讀法？

跟讀法 (Shadowing) 是一種有科學依據的語言學習技巧，最初開發用於專業口譯員的培訓，並由多語言者Alexander Arguelles博士普及。這個方法簡單而強大：您在聽英語母語原聲的同時立即大聲重複——就像是一個延遲1-2秒緊跟說話者的影子。與被動聽力或語法練習不同，跟讀法強迫您的大腦和口腔肌肉同時處理並模模擬實的講話模式。研究表明它能顯著提高發音準確性，語調，節奏，連讀，聽力理解和口語流利度——使其成為雅思口語備考和真實英語交流最有效的方法之一。

影子跟讀法: 閱讀完整分步指南 →

跟讀練習: Grade 11: Conditional Probability - 通過影片學習英語口語

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為什麼要通過這個影片練習口語？

語法與句型分析

常見發音陷阱

影片中的語法

什麼是跟讀法？