Prática de Shadowing: Super Simple Explanation of Probability Tree Diagram! - Aprenda a falar inglês com vídeo
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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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Vocabulário e dicas de fala para esta lição
Esta aula de conversação de nível B1 usa o vídeo “Super Simple Explanation of Probability Tree Diagram!”. As palavras que mais se repetem: probability, blue, marble, probabilities, tree. Este vídeo tem 116 frases e 1569 palavras para praticar shadowing. A fala dura 11:29. O falante mantém um ritmo estável de cerca de 137 palavras por minuto, confortável para o shadowing. 82% das palavras estão entre as 3.000 mais comuns do inglês; vale a pena estudar o restante antes de começar.
Vocabulário principal deste vídeo
As 15 palavras mais avançadas do vídeo, com pronúncia e significado:
| Palavra | Pronúncia | Significado |
|---|---|---|
| probability substantivo | /ˌpɹɑ.bəˈbɪl.ə.ti/ | probabilidade |
| marble substantivo | /ˈmɑɹ.bəl/ | mármore |
| diagram substantivo | /ˈdaɪ.ə.ɡɹæm/ | diagrama |
| multiply verbo | /ˈmʌltɪplaɪ/ | multiplicar |
| calculate verbo | /ˈkælkjʊleɪt/ | calcular |
| coin substantivo | /ˈkoɪ̯n/ | moeda, prata |
| satisfy verbo | /ˈsætɪsfaɪ/ | satisfazer |
| simplify verbo | /ˈsɪmplɪfaɪ/ | simplificar |
| toss verbo | /tɔs/ | jogar, arremessar |
| separately advérbio | /ˈsɛp.ɹət.li/ | separadamente |
| beside | /bɪˈsaɪd/ | irrelevante para |
| manageable adjetivo | /ˈmænəd͡ʒəb(ə)l/ | gerível |
| confuse verbo | /kənˈfjuːz/ | confundir |
| locate verbo | /ˈloʊˌkeɪt/ | localizar |
| randomly advérbio | /ˈɹændm̩li/ | aleatoriamente, ao acaso |
Gramática neste vídeo
As estruturas que o falante mais usa, com as palavras exatas do vídeo:
| Estrutura | No vídeo |
|---|---|
| Voz passiva be + particípio passado — o foco está no que acontece, não em quem faz | are colored · can be seen · is labeled |
| Present continuous am/is/are + -ing — algo que está acontecendo agora ou nestes dias | are following · is selecting · are adding |
| Futuro com “going to” be going to + verbo — um plano ou algo que dá para prever | we're going to learn · is going to roll |
| Futuro com “will” will + verbo — uma decisão, promessa ou previsão | we'll use · will multiply |
Pronúncia para ficar de olho
O falante usa 3 contrações e formas reduzidas, como don't, we'll, we're. Diga-as na forma curta, do jeito que você ouve.
- Palavras longas — acerte a sílaba tônica: probability /ˌpɹɑ.bəˈbɪl.ə.ti/, manageable /ˈmænəd͡ʒəb(ə)l/, altogether /ɔl.tuˈɡɛð.ɚ/
Sons difíceis para falantes de português:
- Consoante final — sem acrescentar um “i” depois: calculate /ˈkælkjʊleɪt/, beside /bɪˈsaɪd/, locate /ˈloʊˌkeɪt/, subscribe /səbˈskɹaɪb/, flip /flɪp/
- /l/ final — a língua toca o céu da boca, não vira “u”: marble /ˈmɑɹ.bəl/, manageable /ˈmænəd͡ʒəb(ə)l/
Como praticar com este vídeo
- Ouça o vídeo inteiro uma vez sem falar e anote as palavras que você não conhece.
- Faça shadowing frase por frase na velocidade normal, repetindo cada uma até o seu ritmo ficar igual ao do falante.
- Grave a sua voz e compare com o original, prestando atenção a palavras como probability, marble, diagram.
O que é a Técnica de Shadowing?
Shadowing é uma técnica de aprendizado de idiomas com base científica, originalmente desenvolvida para o treinamento de intérpretes profissionais. O método é simples, mas poderoso: você ouve áudio em inglês nativo e repete imediatamente em voz alta — como uma sombra seguindo o falante com 1-2 segundos de atraso. Pesquisas mostram melhora significativa na precisão da pronúncia, entonação, ritmo, sons conectados, compreensão auditiva e fluência na fala.