Pratica di Shadowing: Super Simple Explanation of Probability Tree Diagram! - Impara a parlare inglese con i video
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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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Vocabolario e note di pronuncia per questa lezione
Questa lezione di conversazione di livello B1 si basa sul video “Super Simple Explanation of Probability Tree Diagram!”. Le parole che ritornano più spesso: probability, blue, marble, probabilities, tree. Questo video contiene 116 frasi e 1569 parole da ripetere con lo shadowing. Il parlato dura 11:29. Chi parla mantiene un ritmo costante di circa 137 parole al minuto, comodo per lo shadowing. Il 82% delle parole rientra nelle 3.000 più comuni dell’inglese; conviene studiare le altre prima di iniziare.
Vocaboli chiave di questo video
Le 15 parole più avanzate del video, con pronuncia e significato:
| Parola | Pronuncia | Significato |
|---|---|---|
| probability sostantivo | /ˌpɹɑ.bəˈbɪl.ə.ti/ | probabilità |
| marble sostantivo | /ˈmɑɹ.bəl/ | marmo |
| diagram sostantivo | /ˈdaɪ.ə.ɡɹæm/ | diagramma |
| multiply verbo | /ˈmʌltɪplaɪ/ | moltiplicare |
| calculate verbo | /ˈkælkjʊleɪt/ | calcolare |
| spinner sostantivo | /ˈspɪnɚ/ | trottola, girandola |
| coin sostantivo | /ˈkoɪ̯n/ | moneta |
| satisfy verbo | /ˈsætɪsfaɪ/ | soddisfare, accontentare |
| toss verbo | /tɔs/ | tirare un pallonetto, lanciare |
| separately avverbio | /ˈsɛp.ɹət.li/ | distintamente, separatemente |
| manageable aggettivo | /ˈmænəd͡ʒəb(ə)l/ | maneggevole, maneggiabile |
| confuse verbo | /kənˈfjuːz/ | confondere |
| locate verbo | /ˈloʊˌkeɪt/ | localizzare |
| organize verbo | /ˈɔɹɡənaɪz/ | organizzare |
| subscribe verbo | /səbˈskɹaɪb/ | abbonarsi |
La grammatica di questo video
Le strutture che chi parla usa di più, con le parole esatte del video:
| Struttura | Nel video |
|---|---|
| Forma passiva be + participio passato — conta ciò che accade, non chi lo fa | are colored · can be seen · is labeled |
| Present continuous am/is/are + -ing — qualcosa che succede adesso o in questo periodo | are following · is selecting · are adding |
| Futuro con “going to” be going to + verbo — un piano o qualcosa che si vede arrivare | we're going to learn · is going to roll |
| Futuro con “will” will + verbo — una decisione, una promessa o una previsione | we'll use · will multiply |
Pronuncia a cui fare attenzione
Chi parla usa 3 contrazioni e forme ridotte, come don't, we'll, we're. Pronunciale nella forma breve, così come le senti.
- Parole lunghe — attenzione all’accento: probability /ˌpɹɑ.bəˈbɪl.ə.ti/, manageable /ˈmænəd͡ʒəb(ə)l/, altogether /ɔl.tuˈɡɛð.ɚ/
I suoni difficili per chi parla italiano:
- Consonante finale — senza aggiungere una vocale dopo: calculate /ˈkælkjʊleɪt/, toss /tɔs/, beside /bɪˈsaɪd/, confuse /kənˈfjuːz/, locate /ˈloʊˌkeɪt/
- /æ/ — più aperta della “e”: diagram /ˈdaɪ.ə.ɡɹæm/, calculate /ˈkælkjʊleɪt/, satisfy /ˈsætɪsfaɪ/, manageable /ˈmænəd͡ʒəb(ə)l/, randomly /ˈɹændm̩li/
Come esercitarsi con questo video
- Ascolta tutto il video una volta senza parlare e annota le parole che non conosci.
- Fai shadowing frase per frase a velocità normale, ripetendo ognuna finché il tuo ritmo coincide con quello di chi parla.
- Registrati e confronta con l’originale, facendo attenzione a parole come probability, marble, diagram.
Cos'è la tecnica dello Shadowing?
Shadowing è una tecnica di apprendimento delle lingue supportata da studi scientifici, originariamente sviluppata per la formazione dei traduttori professionisti e resa popolare dal poliglotta Dr. Alexander Arguelles. Il metodo è semplice ma potente: ascolti un audio in inglese di madrelingua e lo ripeti immediatamente ad alta voce — come un'ombra che segue il parlante con un ritardo di solo 1–2 secondi. A differenza dell'ascolto passivo o degli esercizi di grammatica, lo shadowing costringe il tuo cervello e i muscoli della bocca a elaborare e riprodurre simultaneamente i modelli di discorso reale. La ricerca dimostra che migliora significativamente la precisione della pronuncia, l'intonazione, il ritmo, il discorso connesso, la comprensione dell'ascolto e la fluidità del parlato — rendendolo uno dei metodi più efficaci per la preparazione alla prova di speaking dell'IELTS e per la comunicazione reale in inglese.