Thank you! It's always disappointing when I finally learn the material that I struggle to understand just to find out that it was actually quite simple.
This requires you to already know how to calculate conditional probability. In the third line, in yellow, you keep re-using the number 0.35, without which you could not have solved the problem. But getting the 0.35 required you to already know how to solve the problem P(A|B) which is already caclulating conditional probability. It doesn't do any good to tell someone that they need to know how to calculate conditional probability before they learn how to calculate conditional probability.
No. P(A and B) was calculated by P(A given B) * P(B). If A and B were independant of each other then P(A and B) would be simply be P(A) * P(B) because neither events affects the outcome of the other event. But because the P(A) changes depending on the outcome of B so we have to take into account this difference when calculating the probability of both events occuring hence we use the value of P(A given B) which incorporates the extra information of the event "B is true". Therefore P(A and B) = P(A given B) * P(B) Then inverse also holds true i.e. P(A and B) = P(B given A) * P(A) Both of these have the common expression P(A and B) on the LHS hence we can equate them. Hence proved P(A given B) * P(B) = P(B given A) * P(A) 3Blue1Brown has a very nice visualisation showing why this is true on his channel.
The biggest thing is writing out what you know. What is P(A)? P(B)? P(A|B) or P(B|A)? They have to give you some information. Once you write out what you know, you can find out what you don't know. Also, making a table helps as well if you are more of a visual person.
The way I was taught P(A and B) was like saying probability of (A and then B) ... From this it makes intuitive sense that it follows P(A) *P(B|A) because A happened first ... Not sure how you can switch it to say P(B) *P(A|B) without switching it to say P(B and A) which we know P(A and B) is not equal to P(B and A)
I was trying to find out how to find P(A and B) and I was searching all of this up on google and kept going in circles without an answer spending 10 minutes struggling. I come here and get the answer in the first 3.5 minutes.
I think you should mention that we´re looking at the events in the day as non-linear space time, just as Einstein saw it, because if you look at it as a regular time line you will get confused. I mean, how does eating pizza for lunch affect the probability of something that ALREADY OCCURRED IN THE PAST, a decision that was already made (i.e. what Rahul ate for his previous breakfast).
I think the biggest problem with probability is English Because this guy was saying find the intercepts given the conditional probability of one side (pause finding the conditional probability is intercept over the sample space of the condition) so to find the interceptor multiply the given the conditional probability and the sample space
Omgness l just about understand this let's see if in two hours time I have managed to retained this information. If l do well l have managed to surprise myself.
I understand it up to 3:40. Can anyone explain it? He says that P(B/A) x P(A) is the equivalent of the aforementioned equation. But isn't P(B/A) what he's TRYING to find? So how can he start including it in the equation? And then he doesn't explain why he divides it by 0.6?
For those who are confused why P(A and B) = P(A | B) * P(B) check out this probability rule. The rule states: P(A|B) = P(A and B) / P(B) So we put P(B) to the left side we get: P(A|B) * P(B) = P(A and B)
The fact that my teacher did horrible with explaining this, left me completely confused, just for me to find this video and realize it is quite rather simple.
I don't understand the conditional probability P (A | B) when you can't eat breakfast before lunch. Doesn't the dependent variable have to come AFTER the independent variable?
P(A and B) = P(B and A). But, P(A | B) does NOT equal P(B | A). P( A | B) = P( A and B)/P(B) --(i) and P(B | A) = P(B and A)/P(A)-- (ii). We are given P(A | B) and to find P( B | A) we need P( B and A). We know that P(B and A) = P(A and B). We find P(A and B) by rearranging the equation i, and use the result as P( B and A).
This is not how I've done it. I actually solved it mentally using the following logic: 1. The probability that B follows A (given that B occured) is 0.7. 2. B happens with a probability of 0.5. 3. The total probability of A occuring is 0.6, out of that, we know that (0.5 * 0.7) is the portion where A precedes B (or, B follows A) since B happens with a probability of 0.5 and once B happens, A has a probability of 0.7 of having occured. Essentially, this maps out as: p(B|A) = p(B) * p(A|B) ______________ p(A) I just hope it's correct. I must admit I struggle a bit with probability. I always try to solve it without formulas, using a problem-solving approach instead (manipulating the problem in my head and going around it)
So the problem said "On a randomly selected day, the probability that Rahul will eat a bagel for breakfast is 0.6, and the probability that he will eat pizza for lunch is 0.5. The conditional probability that he eats a bagel for breakfast, given that he eats pizza for lunch, is equal to 0.7." This is like saying that if Rahul eats a pizza for lunch, the probability of him eating (or having eaten) a bagel for breakfast increases from 0.6 to 0.7. Am I correct?
To many missing information like how’d they come to .6 is he able to eat pizza for breakfast or is it that he can only eat a bagel for breakfast and only pizza for lunch and does he have to eat lunch and breakfast or can he choose to skip them if he can choose it’s just 2 out comes he eats or he doesn’t and also only 2 options of food pizza or bagel
How can we make a conclusion about what Rehul wants for lunch, given that he has decided to have a Bagel for breakfast? Couldn't he have some weird preference for lunch for the specific scenario where he has already had a bagel for lunch?
hey, i have a problem where we are given the probability of A and B only and we are asked to find probability of (A U B) WHICH IS DIFFICULT TO FIND BECUASE WE ARE NOT GIVEN P(B/A) OR P(A/B)
I don't get how P (A and B) is equal to P (A I B)* P(B). If we were counting just P (A and B) we would use just a multiplication formula --> P (A) * P (B) = 0.6*0.5 = 0.30 not 0.35. Can someone explain this please?
How can this example make logical sense? One test subject (Rahul) was observed X number of days to give the probability of A and B happening (distinct values given for each event!). Now A and B are observed to happen on the same day. So how can you have a distinct number such as the value for A occurring and then a distinct number of B occurring GIVEN that they are both dependent on each other happening. I would argue that you could not have this example, A (as given to us here) can be dependent on B but B cannot be dependent on A this would create (in my mind ) a circular argument. How could you observe independent values for A and B if they are both occurring in the same system. If I am right then this is example was created by a none scientist. The only way ( that I can see) someone generating this question is if they have never performed an experiment. Otherwise, you would see the flaw in observing 1 test subject and coming up with Values (A or B) which are "constants" yet dependent on each other. This is an excellent example of how you can use math to get a number that means nothing.
Katherine typically gets two types of alcoholic beverages at the bar. She will either order a midori sour 40% of the time or order an AMF. After her first drink, Katherine can either decide to order a water or another alcoholic beverage. If she orders a midori sour, she decides to get a glass of water 20% of the time and if she orders an AMF, she tends to order a glass of water 55% of the time. If we know that she ordered a water as her second drink, what is the probability that he first drink was an AMF?
The problem stated that the conditional probability of eating a bagel for breakfast is dependent on the probability of eating a pizza for lunch. The problem NEVER stated the possibility of the reverse: that the probability of eating a pizza for lunch could ever depend on the probability of eating a bagel for breakfast. So I don´t follow the logic.
It means what you already know. For example let's say " how many boys are in a classroom of 30 students, Given that 14 students are girls?" So we use what is given to help us find our answer because we already know it's value. So 30-14 = 16 By using what is given we came to the conclusion that there are 16 boys in the class.
I don't understand how come you guys can't just have easier questions or not repeat the same process for each problem coin, deck of cards none of these helping me
Mr Khan, can you please not waste so much time on things you don't need to do, like using different colours and 'mistakenly' using the wrong colour so you can waste time by erasing it and using the correct one. i'm writing an exam tomorrow and i don't have much time, all i'm saying is that the video would've been much shorter and your students could use the time to watch more of your videos, giving you more views. With all due respect. Please don't block me.
I m Rahul, and I approve this 💫
Rahul Bhatt 😂
🤣
😂😂😂😂
rahul got hella cholesterol
Kevin Farrell i
chill
Rahul Rana AHAHHAHA
Ayo blud, man’s hella fit. DONT CHAT TO MAN LIKE THAT 😂
💀
Thank you!
It's always disappointing when I finally learn the material that I struggle to understand just to find out that it was actually quite simple.
IKR
Gosh I’m still confused!! I gotta rewatch this at a later time maybe it would make a difference
Me too haha!
I’m about to have a test on these and im so scared 😭
This requires you to already know how to calculate conditional probability. In the third line, in yellow, you keep re-using the number 0.35, without which you could not have solved the problem. But getting the 0.35 required you to already know how to solve the problem P(A|B) which is already caclulating conditional probability. It doesn't do any good to tell someone that they need to know how to calculate conditional probability before they learn how to calculate conditional probability.
No. P(A and B) was calculated by P(A given B) * P(B).
If A and B were independant of each other then P(A and B) would be simply be P(A) * P(B) because neither events affects the outcome of the other event. But because the P(A) changes depending on the outcome of B so we have to take into account this difference when calculating the probability of both events occuring hence we use the value of P(A given B) which incorporates the extra information of the event "B is true".
Therefore P(A and B) = P(A given B) * P(B)
Then inverse also holds true i.e. P(A and B) = P(B given A) * P(A)
Both of these have the common expression P(A and B) on the LHS hence we can equate them.
Hence proved P(A given B) * P(B) = P(B given A) * P(A)
3Blue1Brown has a very nice visualisation showing why this is true on his channel.
Finally able to understand this topic...... For 5 months been struggling and u just washed it away in a matter of 6 minutes. Thank u
I khan not think of anyone who would explain this like you
I khan da wanna throw up
:0
The biggest thing is writing out what you know. What is P(A)? P(B)? P(A|B) or P(B|A)? They have to give you some information. Once you write out what you know, you can find out what you don't know. Also, making a table helps as well if you are more of a visual person.
Dont get the logic of the formula P(A and B) = P(A|B) * P(B). But this channel is fantastic!
The way I was taught P(A and B) was like saying probability of (A and then B) ... From this it makes intuitive sense that it follows P(A) *P(B|A) because A happened first ... Not sure how you can switch it to say P(B) *P(A|B) without switching it to say P(B and A) which we know P(A and B) is not equal to P(B and A)
Thanks man this is exactly what I need help with. YOU are a life saver my friend! God bless you. You beautiful being!
I was trying to find out how to find P(A and B) and I was searching all of this up on google and kept going in circles without an answer spending 10 minutes struggling. I come here and get the answer in the first 3.5 minutes.
Rahul is an indian, he eats parantha for breakfast and chawal for lunch.
Anannya Saxena that is my exact diet
Indian*
Approved 👍
lol, right !!
totally understand dependent and independent probability now, thanks so much! i have a unit test tomorrow.
I think you should mention that we´re looking at the events in the day as non-linear space time, just as Einstein saw it, because if you look at it as a regular time line you will get confused. I mean, how does eating pizza for lunch affect the probability of something that ALREADY OCCURRED IN THE PAST, a decision that was already made (i.e. what Rahul ate for his previous breakfast).
I think the biggest problem with probability is English
Because this guy was saying find the intercepts given the conditional probability of one side (pause finding the conditional probability is intercept over the sample space of the condition) so to find the interceptor multiply the given the conditional probability and the sample space
Actually you've used Bayes theorem indirectly. This could be a good way to prove Bayes theorem.
Take a shot everytime he says probability ;)
Alcohol poisoning
Thank you very much, this is easy to understand & very helpful!
Who is the teacher. I want him to explain all my math to me. This is so well explained, thank you
this is definitely helpful for this midterm i have in one hour
How'd it go?
@@Bruhplease-t1p good thanks for asking
@@Bruhplease-t1p I finally became a doctor
Omgness l just about understand this let's see if in two hours time I have managed to retained this information. If l do well l have managed to surprise myself.
I never comment but I hope this finds you ... you are the greatest teacher ever
I understand it up to 3:40. Can anyone explain it? He says that P(B/A) x P(A) is the equivalent of the aforementioned equation. But isn't P(B/A) what he's TRYING to find? So how can he start including it in the equation? And then he doesn't explain why he divides it by 0.6?
it is similiar to when x is in a maths equation. you want find that certain x and thats when you start to balance everything out.
@@Naddi_ Thankfully I'll never have to understand this again
@@dannyclub09 lucky, i still have exams this year and i cant wait to burn my maths notes
0.7 / 0.6 = 1,166, and 1,166 x 0.5 = 0,583
Just ate a pizza for lunch! Travelling back in time to eat bagel for breakfast!
thank you, you explained it better than my professor :D!
The ratio of P(A) to P(A\B) is 0.857, which is also the ratio that P(B) is to P(B\A).
Is this true for all cases of dependent probability?
For those who are confused why P(A and B) = P(A | B) * P(B) check out this probability rule.
The rule states: P(A|B) = P(A and B) / P(B)
So we put P(B) to the left side we get: P(A|B) * P(B) = P(A and B)
Man thnx so much, I was struggling with this. But now I found the solution, useful explanation for any similar problem.
VERY informative and simple video.
Thanks. This helped a lot :)
Alhumdulillah I've found this ❤
The fact that my teacher did horrible with explaining this, left me completely confused, just for me to find this video and realize it is quite rather simple.
All Hail Kahn
I don't understand the conditional probability P (A | B) when you can't eat breakfast before lunch. Doesn't the dependent variable have to come AFTER the independent variable?
#blessKahn I thought I was gonna fail my stats test , lol I prob will but at least I'll get a higher score than I would've if I didn't study 😂
Did you fail?
You sir are awesome 🙏🏻🙏🏻
thanks, helped a lot
This is so complicatedddd like it just isn’t clicking in my head
The way I did it was
P(A|B)= P(A and B)/P(B)
That gave P(A and B)= 0.35
So P(B|A)= P(A and B)/P(A)
O.35/0.6 = 0.58333
Thank you very much.
P(A and B) = P(B and A). But, P(A | B) does NOT equal P(B | A). P( A | B) = P( A and B)/P(B) --(i) and
P(B | A) = P(B and A)/P(A)-- (ii). We are given P(A | B) and to find P( B | A) we need P( B and A). We know that P(B and A) = P(A and B). We find P(A and B) by rearranging the equation i, and use the result as P( B and A).
use this 2 formula p(A/B)=p(A and B)/p(b)
and
p(A and B)=p(A)*p(B/A)
what is the program used here?
exam in 2 weeks!
dylan what up
Where does the .05, .06 & .07 come from to begin with?
Steve Friedlander the problem above mate. it gives you those numbers.
Read my man
This is not how I've done it. I actually solved it mentally using the following logic:
1. The probability that B follows A (given that B occured) is 0.7.
2. B happens with a probability of 0.5.
3. The total probability of A occuring is 0.6, out of that, we know that (0.5 * 0.7) is the portion where A precedes B (or, B follows A) since B happens with a probability of 0.5 and once B happens, A has a probability of 0.7 of having occured.
Essentially, this maps out as:
p(B|A) = p(B) * p(A|B)
______________
p(A)
I just hope it's correct. I must admit I struggle a bit with probability. I always try to solve it without formulas, using a problem-solving approach instead (manipulating the problem in my head and going around it)
Thanks so much I understand it
Neat. Cool. Thanks.
So the problem said "On a randomly selected day, the probability that Rahul will eat a bagel for breakfast is 0.6, and the probability that he will eat pizza for lunch is 0.5. The conditional probability that he eats a bagel for breakfast, given that he eats pizza for lunch, is equal to 0.7."
This is like saying that if Rahul eats a pizza for lunch, the probability of him eating (or having eaten) a bagel for breakfast increases from 0.6 to 0.7.
Am I correct?
Makes no sense
Me also.
🗿🗿
Came to study probability, left wondering if i am obese 😞
very useful
What’s the probability that (B) will happen if (A) doesn’t happen
To many missing information like how’d they come to .6 is he able to eat pizza for breakfast or is it that he can only eat a bagel for breakfast and only pizza for lunch and does he have to eat lunch and breakfast or can he choose to skip them if he can choose it’s just 2 out comes he eats or he doesn’t and also only 2 options of food pizza or bagel
this video confused me even more thanks
I did it faster by 0.7 / 0.6 = 1,166, and 1,166 x 0.5 = 0,583
Why does P(A|B)*P(B)? This is not explained.
same thoughts. the irony when he said that P(A|B) is dependent to P(A).
How can we make a conclusion about what Rehul wants for lunch, given that he has decided to have a Bagel for breakfast? Couldn't he have some weird preference for lunch for the specific scenario where he has already had a bagel for lunch?
we can also solve this using bayes theorem?
Why does the audio of every video but Khan Academy videos play!? KHAAAAAAAAAAAAAAAAAAAN!!!!!
This is so damn good!!! Thank very much!
hey, i have a problem where we are given the probability of A and B only and we are asked to find probability of (A U B) WHICH IS DIFFICULT TO FIND BECUASE WE ARE NOT GIVEN P(B/A) OR P(A/B)
I don't get how P (A and B) is equal to P (A I B)* P(B). If we were counting just P (A and B) we would use just a multiplication formula --> P (A) * P (B) = 0.6*0.5 = 0.30 not 0.35. Can someone explain this please?
Hi! Did you find the answer to your question ?
The probability that Rahul will eat Bagel Bites for every meal is 100%
i'm rahul and i can confirm that i love bagels and pizzas 👍
This doesn't make sense
It does, though.
3:32 it says "I hope this makes sense" what if it doesn't? I don't get it either.
It does, dough.
Same
Tyshon White It does, though.
I have a question. What's is the probability that rahul eats pizza for dinner if he had it for lunch? considering same probabilities.
AMC ; AIME ; IMO ... Pleaase !!
How can this example make logical sense? One test subject (Rahul) was observed X number of days to give the probability of A and B happening (distinct values given for each event!). Now A and B are observed to happen on the same day. So how can you have a distinct number such as the value for A occurring and then a distinct number of B occurring GIVEN that they are both dependent on each other happening. I would argue that you could not have this example, A (as given to us here) can be dependent on B but B cannot be dependent on A this would create (in my mind ) a circular argument. How could you observe independent values for A and B if they are both occurring in the same system. If I am right then this is example was created by a none scientist. The only way ( that I can see) someone generating this question is if they have never performed an experiment. Otherwise, you would see the flaw in observing 1 test subject and coming up with Values (A or B) which are "constants" yet dependent on each other. This is an excellent example of how you can use math to get a number that means nothing.
Katherine typically gets two types of alcoholic beverages at the bar. She will either order
a midori sour 40% of the time or order an AMF. After her first drink, Katherine can
either decide to order a water or another alcoholic beverage. If she orders a midori sour,
she decides to get a glass of water 20% of the time and if she orders an AMF, she tends
to order a glass of water 55% of the time. If we know that she ordered a water as her
second drink, what is the probability that he first drink was an AMF?
60% with the given Info
why does he multiply P(A|B) x P(B) and not add them instead?
They really just used B for Pizza instead of B for the Bagel
There are more things but I won't mention them cause I don't want to be 'That guy', I probably already am but...
The problem stated that the conditional probability of eating a bagel for breakfast is dependent on the probability of eating a pizza for lunch.
The problem NEVER stated the possibility of the reverse: that the probability of eating a pizza for lunch could ever depend on the probability of eating a bagel for breakfast. So I don´t follow the logic.
Can someone explain me what does "given" in math mean? A was not able to find out how to translate it to my language.
It means what you already know. For example let's say " how many boys are in a classroom of 30 students, Given that 14 students are girls?"
So we use what is given to help us find our answer because we already know it's value.
So 30-14 = 16
By using what is given we came to the conclusion that there are 16 boys in the class.
Enoch Johnson Thanks.
why does rahul eat lunch before breakfast?
P(A & B)=0.3..... not 0.35?
so it should be 0.5?
half of all lunches that R eats is pizza haha
rahul is eating like its his last day on earth lol or he has a probability test tmr
This isn't really relevant, but why would they make Bagel for Breakfast A instead of B?
I was thinking the same, but yeah no big deal.
What is the probibility that in an exam the guy in the question will have an Arabic name?
Ricky Wheeler rabu! is Indian name
Ricky Wheeler rahul *
next time please give us the formula first then work through the example instead of expecting us to work through it without the formula - thanks
0.5 divide by 0.6 x 0.7 lol
divided again by 100 will give you 0.583333333 THANKS THAT WAS SO MUCH EASIER - my one question is this, how did he get 0.7 from 0.5 & 0.6?
how do you get 0.7?
+Robert Surrett it is in the question
why u make it so complec. just use Bayes theorem.
he just gave the intuition for it. People like you don't understand how and why something works and are almost like machines.
Ra-HOOOL
where the heck did he get 0.35?
im still confused
You calculate bayes and not conditional probability my friend
This is still soo hard to understand 😭
Just ok🤨
What? ! I'm so lost
dont say a and b say the example meaning
I don't understand how come you guys can't just have easier questions or not repeat the same process for each problem
coin, deck of cards none of these helping me
QUIT REPEATING YOURSELF. WASTES SO MUCH TIME
Don’t make sense
Бред
Mr Khan, can you please not waste so much time on things you don't need to do, like using different colours and 'mistakenly' using the wrong colour so you can waste time by erasing it and using the correct one. i'm writing an exam tomorrow and i don't have much time, all i'm saying is that the video would've been much shorter and your students could use the time to watch more of your videos, giving you more views. With all due respect. Please don't block me.