Практика Shadowing: Super Simple Explanation of Probability Tree Diagram! - Изучайте разговорный английский по видео
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Today we're going to learn a probability tree diagram.
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Imagine a spinner that has six equal sections.
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Two sections are colored blue, while the remaining four sections are colored red.
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A student named Jake spins this spinner twice.
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Our first goal is to simply list every possible outcome that can happen after the two spins.
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Since Jake spins the spinner two times, each spin has only two possible outcomes.
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The spinner can land on blue or red during the first spin, and once again on blue or red during the second spin.
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If we write every possible combination, we get four outcomes in total.
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These are blue followed by blue, blue followed by red, red followed by blue, and finally red followed by red.
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Writing all the outcomes like this is manageable for a small example, but as the number of events increases, the list quickly becomes long and confusing.
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This is exactly why we use a probability tree diagram.
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Instead of writing every possibility separately, we organize them into branches so that every possible outcome can be seen clearly.
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We always begin with a single starting point.
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Since the first spin has only two possible outcomes, we draw two branches coming out from this point.
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One branch represents blue, while the other branch represents red.
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These two branches account for every possible result of the first spin.
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Now we move to the second spin.
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No matter what happened on the first spin, the second spin can again result in either blue or red.
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Therefore, from each existing branch, we draw two more branches.
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One branch represents blue and the other represents red.
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If we now trace every complete path from left to right, we obtain exactly the same four outcomes we listed earlier.
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The first path represents blue, followed by blue.
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The second path represents blue, followed by red.
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The third path represents red, followed by blue.
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The final path represents red, followed by red.
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At this point, the tree diagram shows every possible outcome, but it does not yet include any probabilities.
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To add those, we first look at the spinner.
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Since two of the six sections are blue, the probability of landing on blue is 2 out of 6, which simplifies to 1 out of 3.
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The remaining four sections are red, so the probability of landing on red is four out of six, which simplifies to two out of 3.
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We now write these probabilities beside each branch of the tree.
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Every branch representing blue is labeled 1 out of 3, while every branch representing red is labeled 2 out of 3.
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Since the same spinner is used again for the second spin, these probabilities remain exactly the same on every second level branch.
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Our probability tree diagram is now complete.
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It shows every possible outcome together with the probability of taking each branch.
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Now let's look at another example where we'll use a probability tree diagram to calculate probabilities.
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A student named Emily is going to roll a fair six-sided die and then flip a fair coin.
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She wins a prize only if she rolls a four on the die and then gets heads on the coin toss.
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Our task is to complete the probability tree diagram.
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Okay, we begin by looking at the die.
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There are only two possible outcomes that matter for this question.
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Emily either rolls a four or she does not roll a four.
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Since there is only one face showing four on a fair six-sided die, the probability of rolling a four is one out of six.
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The remaining five faces are not four, so the probability of not rolling a four is five out of six.
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We write these probabilities on the first pair of branches.
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Together, they add up to one, as they always should.
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Now we move to the second stage of the tree diagram, which represents the coin toss.
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From each of the two branches that we have already drawn, we again draw two new branches.
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One branch represents heads, while the other represents tails.
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This is because after either rolling a four or not rolling a four, the coin can still land on either heads or tails.
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A fair coin has two equally likely outcomes, heads and tails.
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Therefore, the probability of getting heads is one out of two, and the probability of getting tails is also one out of two.
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We write these probabilities on both sets of second-level branches because the coin is fair regardless of the result of the die.
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Our probability tree diagram is now complete.
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The next step is to use this tree diagram to calculate the probability of different outcomes.
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Suppose we want to calculate the probability that Emily wins the prize.
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According to the question, she wins only if she first rolls a four and then gets heads.
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We begin by locating this root on the tree diagram.
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First, we follow the branch labeled 4, and then we follow the branch labeled heads.
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Whenever we want to find the probability of one complete root through a probability tree, we multiply the probabilities along that root.
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So in this example, we will multiply 1 by 6 and half.
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This is the fundamental rule that is used in every probability tree question.
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This gives us 1 by 12.
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Therefore, the probability that Emily wins the prize is 1 out of 12.
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Amazing!
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Now let's look at one last example involving probability tree diagrams.
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A bag contains 4 blue marbles and 6 yellow marbles.
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A student named Michael randomly picks one marble from the bag, replaces it, and then picks another marble.
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We need to complete the probability tree diagram and answer a few probability questions.
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Since there are two possible outcomes for the first pick, blue or yellow, we begin by drawing two branches from the starting point.
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Now we move to the second pick.
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Because the second pick can again result in either blue or yellow, we draw two more branches from each of the first branches.
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This gives us all the possible outcomes for the two picks.
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Now, the first step is to determine the probabilities for the first pick.
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Since there are four blue marbles and six yellow marbles, there are ten marbles altogether.
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Therefore, the probability of picking a blue marble is four out of 10,
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while the probability of picking a yellow marble is 6 out of 10.
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These probabilities are written on the first pair of branches.
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Then we write the probabilities for the second pick.
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Since the first marble is placed back into the bag before the next pick, the contents of the bag remain exactly the same.
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Therefore, the probability of picking a blue marble is still 4 out of 10,
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while the probability of picking a yellow marble is still 6 out of 10.
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We write these probabilities beside each of the second-level branches, and our probability tree diagram is now complete.
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Next, suppose we are asked to calculate the probability that both marbles selected are blue.
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We first identify the correct root on the tree diagram?
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This route follows the blue branch on the first pick and then the blue branch on the second pick.
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Since we are following one complete route, we multiply the probabilities along that path.
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The probability of blue followed by blue is 4 out of 10 multiplied by 4 out of 10.
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Therefore, the probability of selecting two blue marbles is 16 out of 100, which is 16%.
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Now here's how this question becomes more interesting and fun.
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Suppose we are asked to calculate the probability of selecting exactly one blue marble.
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There are two different ways this can happen.
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The first possibility is selecting blue on the first pick and yellow on the second pick.
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The second possibility is selecting yellow on the first pick and blue on the second pick.
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Let us calculate the probability for the first route.
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The probability of blue followed by yellow is 4 out of 10 multiplied by 6 out of 10, which is 24 out of 100.
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Now consider the second possible route.
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The probability of yellow followed by blue is 6 out of 10 multiplied by 4 out of 10, which is 24 out of 100.
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Since both of these routes satisfy the condition of selecting exactly one blue marble, we must add their probabilities together.
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24 by 100 plus 24 by 100 equals 48 out of 100.
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Notice that this time we are adding the probabilities because there is more than one successful route.
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Whenever multiple different paths satisfy the required condition, we add their probabilities together.
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Finally, suppose we are asked to calculate the probability that both selected marbles are the same color.
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There are again two successful routes.
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The first route is blue followed by blue, while the second route is yellow followed by yellow.
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Since both roots satisfy the condition, we calculate each one separately.
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We already know that the probability of blue followed by blue is 16 out of 100.
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The probability of yellow followed by yellow is 6 out of 10 multiplied by 6 out of 10
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or 36 out of 100.
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Since both roots produce marbles of the same color, we add their probabilities together.
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16 by 100 plus 36 by 100 equals 52 out of 100.
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This is the probability that both selected marbles have the same color.
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And that's how probability tree diagrams work.
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Just remember the two key rules.
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Multiply probabilities along a single path and add the probabilities of different successful paths.
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If you enjoyed this video, please don't forget to like, share, and subscribe to our channel.
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Also, you can support my channel by joining our community and becoming a member. So good!
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Лексика и советы по произношению к этому уроку
Этот урок разговорной практики уровня B1 построен на видео «Super Simple Explanation of Probability Tree Diagram!». Чаще всего повторяются слова: probability, blue, marble, probabilities, tree. В этом видео 116 предложений и 1569 слов для шедоуинга. Речь длится 11:29. Говорящий держит ровный темп — около 137 слов в минуту, удобный для шедоуинга. 82% слов входят в 3000 самых частых слов английского языка; остальные стоит разобрать перед занятием.
Ключевая лексика этого видео
Самые сложные слова из видео (15), с произношением и значением:
| Слово | Произношение | Значение |
|---|---|---|
| probability существительное | /ˌpɹɑ.bəˈbɪl.ə.ti/ | вероя́тность, правдоподо́бие |
| marble существительное | /ˈmɑɹ.bəl/ | мра́мор |
| diagram существительное | /ˈdaɪ.ə.ɡɹæm/ | план, диагра́мма |
| multiply глагол | /ˈmʌltɪplaɪ/ | приумно́жить |
| calculate глагол | /ˈkælkjʊleɪt/ | вычисля́ть, вы́числить |
| coin существительное | /ˈkoɪ̯n/ | моне́та |
| satisfy глагол | /ˈsætɪsfaɪ/ | удовлетворя́ть, удовлетвори́ть |
| simplify глагол | /ˈsɪmplɪfaɪ/ | упроща́ть, упрости́ть |
| toss глагол | /tɔs/ | броса́ть, подбра́сывать |
| separately наречие | /ˈsɛp.ɹət.li/ | отде́льно, врознь |
| beside | /bɪˈsaɪd/ | поми́мо |
| confuse глагол | /kənˈfjuːz/ | пу́тать, запу́тать |
| locate глагол | /ˈloʊˌkeɪt/ | помести́ть |
| organize глагол | /ˈɔɹɡənaɪz/ | организо́вывать, организова́ть |
| subscribe глагол | /səbˈskɹaɪb/ | подпи́сывать, подписа́ть |
Грамматика в этом видео
Конструкции, которые говорящий использует чаще всего, с точными словами из видео:
| Конструкция | В видео |
|---|---|
| Пассивный залог be + причастие прошедшего времени — важно, что происходит, а не кто это делает | are colored · can be seen · is labeled |
| Present Continuous am/is/are + -ing — то, что происходит сейчас или в эти дни | are following · is selecting · are adding |
| Будущее с «going to» be going to + глагол — план или то, что явно произойдёт | we're going to learn · is going to roll |
| Будущее с «will» will + глагол — решение, обещание или прогноз | we'll use · will multiply |
Произношение, на которое стоит обратить внимание
Говорящий использует 3 сокращённых и редуцированных форм, например don't, we'll, we're. Произносите их коротко, так, как слышите.
- Длинные слова — следите за ударением: probability /ˌpɹɑ.bəˈbɪl.ə.ti/, manageable /ˈmænəd͡ʒəb(ə)l/, altogether /ɔl.tuˈɡɛð.ɚ/
Звуки, трудные для русскоязычных:
- Звонкие согласные в конце слова — не оглушайте их: beside /bɪˈsaɪd/, confuse /kənˈfjuːz/, organize /ˈɔɹɡənaɪz/, subscribe /səbˈskɹaɪb/, involve /ɪnˈvɑlv/
Как заниматься с этим видео
- Прослушайте всё видео один раз молча и выпишите незнакомые слова.
- Повторяйте предложение за предложением на обычной скорости, пока ваш ритм не совпадёт с ритмом говорящего.
- Запишите себя и сравните с оригиналом, обращая внимание на такие слова, как probability, marble, diagram.
Что такое техника Shadowing?
Shadowing — это научно обоснованная техника изучения языка, изначально разработанная для подготовки профессиональных переводчиков и популяризированная полиглотом доктором Александром Аргуэльесом. Метод прост, но эффективен: вы слушаете аудио на английском от носителей языка и немедленно повторяете вслух — как тень, следующая за говорящим с задержкой в 1–2 секунды. В отличие от пассивного прослушивания или грамматических упражнений, Shadowing заставляет мозг и мышцы рта одновременно обрабатывать и воспроизводить реальные речевые паттерны. Исследования показывают, что это значительно улучшает точность произношения, интонацию, ритм, связную речь, понимание на слух и беглость речи — что делает его одним из самых эффективных методов для подготовки к IELTS Speaking и реального общения на английском.