शैडोइंग अभ्यास: Quant Interview Questions #2 | Bayes Theorem - वीडियो के साथ अंग्रेजी बोलना सीखें

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You have a bucket of 500 coins.

499 on normal coins?

but one of them is a double -headed coin.

You draw a coin randomly for the bucket and then you flip it five times.

Question one.

If you picked a normal coin, so if you drew a normal coin, What is the probability of flipping 5 hints?

Question 2: What is the probability of flipping 5 heads?

in general, just from the situation.

And lastly, What is the probability of picking a normal coin having obtained 5 hits from flipping the coin that was drawn.

Now from this last question, you can tell that we are trying to calculate a probability

using or knowing some new piece of information in this case is the knowledge that we have flipped Five hits.

using this random coin.

Hence, this is a question regarding Bayes' theorem listed on the right.

So the probability of A of event A given event B is equal to the probability of event A, so known as the prior,

And this is scaled by some fraction, which is the probability of event B given A.

normalized or divided by the probability of event B.

So, To break down this equation, we can think of it as the posterior, so our posterior estimate of probabilities, In this case, the posterior estimate of

The probability of event A on the left is equals to the prior estimate of this, which is just probability of event A,

And this is scaled by some you could think about it scaling coefficient.

And this is represented by the fraction.

Now.

At this point, I like to just write out all the probabilities

that I can just obtain just from the question description itself.

So, Here we have some Straightforward ones, the probability of picking a normal coin, there are 499 of them out of the 500.

Therefore, it's 499 over 500 and the probability of picking a double -headed coin, which is 1 out of 500.

Now focusing on a normal coin, what is the probability of having a heads or tails, right?

Because this is a normal coin, we only have two outcomes for when we flip one, a heads or tails.

and you will agree that it is half and half for both of them, because it's a fair coin, a fair coin or normal coin in this case.

Whereas for the double -headed coin, because it is double -headed, the only outcome you can get is hits.

Therefore, the probability of drawing a hit or flipping a hit using a double -headed coin, or in mathematical speaks, the probability of Flipping ahead.

Given that you have a double -headed coin, It's just 1 because you'll always get it.

And the probability of getting tails, having the double -headed coin, is obviously 0 because it's double -headed.

So let's address question one.

If we pick a normal coin, what is the probability of flipping 5 hits with this normal coin?

So we flip it once, twice, 4 times, 5 times, what is the probability of getting 5 hits?

Now because these are five flips, 5 independent flips, so each flip does not affect the other

we can say that the probability of having 5 hits given that we have a normal coin is just Half?

times half, times half, times half, five times.

1 /2 to the power of 5, which is just 1 /32, right?

Because these are five independent flips, each of them having, with each outcome having an equal opportunity of occurring.

And you can also say that the probability of getting 5 Tails will be the same thing, right?

Because the probability of getting a hit full of tails on a normal coin is the same.

And for the sake of completeness, let's also calculate the above but for a double -headed coin.

So the probability of getting 5 hits Assuming you have a double -headed coin, it's naturally just 1.

because you're always going to get ahead with a double -headed coin, therefore it's 1 to the power of 5, which is just 1.

So that answers the first question.

The probability of getting 5 /8 given that we have a normal coin is 1 /32.

Thank you.

Now for the second question.

What is the probability of flipping 5 hits?

So we know that we have flipped.

a coin five times, right?

This coin could either be a double headed coin or a normal coin so

what is the probability of us just getting 5 hits, regardless of what type of coin we have?

So we can say

And I hope you are following

that the probability of getting 5 hits is the probability of getting 5 hits with a normal coin.

plus the probability of getting 5 hits with a double -headed coin.

Breaking that down further with more mathematical notation, it is the probability of getting 5 hits,

It's probably the event of 5 hits intersected with the event of getting a normal coin,

plus the probability of The event of five hits intersected with the event of getting a double -headed coin.

And breaking this down further using the laws of conditional probability, we can see that these two terms here.

these two terms here break down into these two terms here, alright?

using this equation here.

So, Let's think about what we have, right?

On the left, Here, we have the probability of getting 5 hits, given we have a normal coin, multiply by the probability of having a normal coin.

And similarly for the second term, And if you think about it, we already have all these probabilities.

This is what's listed above us.

hence it's plugging in the values, we should get this.

1 over 32 times 499 over 500 plus 1, times 10500, which gives us 0 .03318, right?

So this is the probability of getting 5 hints.

Okay.

Hence, Going back to our question, And going back to our last question,

One is the probability of picking a normal coin, having obtained 5 hits from flipping the drawn coin.

So expressing that in mathematical terms is the probability of getting A Nullo coin?

given that we have flipped 5 hits.

So using Bayes' theorem, we can break this down into the probability of getting a normal coin,

our prior multiplied by this scaling coefficient, this fraction.

So it's the probability of getting 5 hits given that we have a normal coin.

normalized by the probability of getting 5 hits in general. and These

three terms we have already calculated from

either the question itself based on the description or from parts one and two above so just plugging in the values

we will see that The answer for part 3 is 0 .9399.

Great.

You've answered the question.

Thank you.

At this point, the interviewer may now ask you, does this result make sense?

Why or why not?

So let's think about what we have so far.

So we started with a prior, and we started with a prior estimate of Flipping.

um, Sorry, we started with a prior of the probability of getting a normal coin here,

which is just 499 out of 500 because there are 499 coins normal coins out of 500 coins.

And then we drew a coin and we had some new information about this having flipped five hits, So let's think about it.

Now our posterior, estimate of probability of getting a normal coin, is 0 .9399.

Right.

And if we just express the prior in a decimal form, just to make it easier for us, What we have is...

The probability of getting a normal coin, the prior, is 0 .998.

And now what you will notice is that our posterior 9399 is lower than our prior.

0 .998.

100

Why?

101

Why has the posterior changed and lower it, lower slightly compared to our prior.

102

So let's think about what this new information is.

103

This new information that was given to us was that we obtained 5 hits.

104

Right?

105

Yeah. And...

106

The fact that we obtain 5 heads, this New information.

107

actually supports the other outcome which is us having a double -headed coin.

108

because the probability of getting a...

109

of flipping 5 hits using a normal coin is so much rarer compared to that of a double headed coin,

110

that this new information that we have is actually supporting the fact that we might actually have a double -headed coin.

111

Therefore, this Um, posterior estimate of the probability of getting a normal coin has dropped.

112

It's dropped a little bit, Why?

113

Why did they drop a little bit?

114

Because Overwhelmingly, most of the coins are still normal coins.

115

Therefore, it's still likely that we have drawn a normal coin.

116

but it's dropped a little bit because we know that this new evidence doesn't support us having drawn a normal coin.

117

It actually supports us having likely drawn a double -headed coin.

118

Hence, we see this very small drop in the from the prior to the posterior estimate.

119

Now, depending on the I guess the structure of the question,

120

you might actually see that this prior to posterior drop in probabilities or maybe increase, depending on the question, can actually be quite large.

121

And if you want such a question, please refer to The other base question that's found on this playlist on the left

122

And if you would like to learn more about my recent experience and also my mistakes from my recent quantum interviews, applying in London in the year 2020.

123

3. please refer to the playlist on the right.

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And don't forget to like and subscribe.

125

Thank you.

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इस वीडियो के साथ बोलने का अभ्यास क्यों करें?

इस वीडियो में प्रस्तुत विषय 'Bayes Theorem' न केवल गणितीय अवधारणाओं को समझने में मदद करता है, बल्कि यह आपकी अंग्रेजी बोलने का अभ्यास करने का एक बेहतरीन अवसर भी प्रदान करता है। जब आप वीडियो को बार-बार सुनते हैं और बोलने का अभ्यास करते हैं, तो आप तकनीकी शब्दों और जटिल विचारों को भी सरलता से इंगित और समझ सकते हैं। यह प्रक्रिया आपके आत्म-विश्वास को बढ़ाने में मदद करती है और अंग्रेजी शैडोइंग के माध्यम से आप अपने उच्चारण को बेहतर बनाने की दिशा में भी अग्रसर होते हैं।

संदर्भ में व्याकरण और अभिव्यक्तियाँ

Probability of event: "What is the probability of..." जैसे वाक्यांशों का प्रयोग किया गया है, जो किसी घटना की संभावना पूछने में सहायक होते हैं। यह विभाजन आपको संभावना की गणना में मदद करता है।
Conditional statements: "given that you have..." का उपयोग यह दर्शाता है कि किसी घटना की संभावनाएं किस शर्त पर निर्भर करती हैं। यह आपकी बातचीत में जटिल विचार प्रस्तुत करने की क्षमता को बढ़ाता है।
Ratios: "499 out of 500" जैसी अभिव्यक्तियाँ आपको अंश और भागफल को अंकित करने में मदद करती हैं, जो तार्किक विचारों को प्रस्तुत करने के लिए महत्वपूर्ण हैं। इस प्रकार की व्याकरण कौशल आपके संवाद में स्पष्टता लाती है।
Mathematical expressions: "1/2 to the power of 5" जैसे वाक्यांश न केवल गणितीय विचार प्रस्तुत करते हैं, बल्कि आपके उच्चारण के दौरान सही शब्दों को चुनने की संभावना को भी सुधारते हैं।

सामान्य उच्चारण के जाल

इस वीडियो में चर्चा के दौरान कुछ शब्दों का उच्चारण विशेष ध्यान देने योग्य है:

Probability: यह शब्द अक्सर गलत उच्चारित किया जाता है। सही उच्चारण 'प्रॉबैबिलिटी' है।
Coin: 'क्वाइन' की जगह 'कॉइन' का उच्चारण करना महत्वपूर्ण है।
Heads/Tails: जब आप इन शब्दों का उच्चारण करते हैं, तो सुनिश्चित करें कि आप स्पष्टता बनाए रखें, क्योंकि ये शब्द बातचीत में अक्सर इस्तेमाल होते हैं।

इस प्रकार, आप अंग्रेजी उच्चारण में सुधार के लिए यूट्यूब से अंग्रेजी सीखने का सहारा ले सकते हैं। वीडियो को सुनकर वास्तव में ज्ञानपूर्ण सामग्री के माध्यम से प्रभावी शैडोइंग का अभ्यास करें।

इस वीडियो का व्याकरण

वक्ता जिन संरचनाओं का सबसे अधिक प्रयोग करता है, वीडियो के असली शब्दों के साथ:

संरचना	वीडियो में
Present perfect have/has + past participle — बीता हुआ काम जिसका असर अभी भी है	have flipped · have already calculated · You've answered
Passive voice be + past participle — ज़ोर इस पर कि क्या होता है, न कि कौन करता है	was drawn · is scaled · is represented
Relative clauses who / which + उपवाक्य — व्यक्ति या वस्तु के बारे में अतिरिक्त जानकारी	fraction, which is · this, which is · coin, which is

शैडोइंग तकनीक क्या है?

शैडोइंग (Shadowing) एक विज्ञान-समर्थित भाषा सीखने की तकनीक है जो मूल रूप से पेशेवर दुभाषिया प्रशिक्षण के लिए विकसित की गई थी। विधि सरल लेकिन शक्तिशाली है: आप मूल अंग्रेज़ी ऑडियो सुनते हैं और तुरंत इसे ज़ोर से दोहराते हैं — जैसे वक्ता की छाया 1-2 सेकंड की देरी से। शोध से पता चलता है कि यह उच्चारण सटीकता, स्वर, लय, जुड़ी हुई ध्वनियाँ, सुनने की समझ और बोलने की प्रवाहशीलता में काफ़ी सुधार करता है।

शैडोइंग तकनीक: पूरी चरण-दर-चरण गाइड पढ़ें →

शैडोइंग अभ्यास: Quant Interview Questions #2 | Bayes Theorem - वीडियो के साथ अंग्रेजी बोलना सीखें

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इस वीडियो के साथ बोलने का अभ्यास क्यों करें?

संदर्भ में व्याकरण और अभिव्यक्तियाँ

सामान्य उच्चारण के जाल

इस वीडियो का व्याकरण

शैडोइंग तकनीक क्या है?