शैडोइंग अभ्यास: Grade 11: Conditional Probability - YouTube के साथ अंग्रेजी बोलना सीखें

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शैडोइंग नियंत्रण
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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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आप इस वीडियो के माध्यम से यूट्यूब से अंग्रेजी सीखें के तहत अंग्रेजी बोलने का अभ्यास कर सकते हैं। इस वीडियो में शर्तीय संभावना (Conditional Probability) के विषय को समझाया गया है, जो संख्याओं को समझने का एक महत्वपूर्ण हिस्सा है। बोलने का अभ्यास करना न केवल आपकी भाषा को सुदृढ़ बनाता है, बल्कि यह आपको गणितीय विचारों को व्यक्त करने और समझाने में भी मदद करता है। जब आप इस वीडियो की दोहराई करने का प्रयास करते हैं, तो आप अपनी उच्चारण और वाक्य निर्माण में सुधार कर सकते हैं। यह shadow speech तकनीक का उपयोग करके आपकी बोलने की क्षमता को और बेहतर बनाएगा।

व्याकरण और संदर्भ में अभिव्यक्तियाँ

  • "Probability is just about figuring out how likely something is to happen" - यह वाक्य संरचना आपको संभाव्यता के अर्थ को स्पष्ट करने में मदद करती है।
  • “This is a conditional probability” - यहाँ पर शर्तीय संभावना की स्पष्टता को रेखांकित किया गया है, जो बच्चों के लिए एक महत्वपूर्ण विचार है।
  • “So the probability of A given B” - यह उदाहरण एक महत्वपूर्ण संरचना है, जहाँ पहले से ज्ञात जानकारी का उपयोग किया जाता है।
  • “Given that they play football” - यह अभिव्यक्ति वर्तमान तथ्य को देखते हुए संभावनाओं को स्पष्ट करने का एक अच्छा तरीका है।

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