Intro to Conditional Probability | Probability Theory
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- Опубликовано: 30 сен 2024
- What is conditional probability? How does the probability of an event change if we know some other event has occurred? In today’s video math lesson, we go over an intro to conditional probability, introducing the term, the definition, the conditional probability formula, and more with examples and in depth explanation!
Here’s an example of conditional probability: the probability that a RUclips video is about conditional probability, given that it has “Conditional Probability” in the title. You used the fact that this probability is quite high in order to find and or choose this video to teach you about probability! Titles don’t always tell the truth, but since this video had conditional probability in the title and thumbnail, you figured it’s probably gonna teach you about conditional probability, and you were right!
The conditional probability of A given B is written P( A | B ) and is equal to P( A intersect B ) / P( B ). If we know B occurs, then A can only occur where B also occurs, which is why we take the probability of A intersect B. But we are measuring that probability against a reduced sample space where B occurs, so to account for that we divide by P(B).
SOLUTION TO PRACTICE EXERCISE:
We are given that 40% of students pass Exam 1 and 10% of students pass both exams. We want to know the percentage of students that pass both exams, given they have passed Exam 1. For starters, our two events are…
A: Student passes Exam 1
B: Student passes both Exams
We want to know P( B | A ), which is equal to P( B intersect A ) / P( A ). What is P( B intersect A )? The probability that student a passes both exams and the student passes Exam 1 is just the probability that the student passes both exams, which we know is 10%. What is P( A )? The probability that a student passes Exam 1 is given to us as 40%. So P( B | A ) = 10% / 40% = 0.25 or 1/4.
If you are preparing for Probability Theory or in the midst of learning Probability Theory, you might be interested in the textbook I used when I learned Probability Theory. It is "A First Course in Probability Theory" by Sheldon Ross. Check out the book and see if it suits your needs! You can purchase the textbook using the affiliate link below which costs you nothing extra and helps support Wrath of Math!
PURCHASE THE BOOK: amzn.to/2Z8MrB7
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Take
E1 - the students who passed both exam
E2 - the students who passed first exam
E2 is given, so,
P(E1|E2)=P(E1 and E2)÷P(E2)
=10%÷40%
Which gives 0.25
Thanks for the video.
Precisely, great work! You're very welcome and thank you for watching and for the request! My lesson on the law of total probability is rendering now, it will probably be published tomorrow.
Thanks bro !
I thought that 40% was E1 and that we were searching P(E2|E1). I still got the right answer tho.
@w花b this is the right one
The answer is 1/4 or 0.25
Could you do some conditional expectation word problems? Or conditional expectation in general?
THANK YOU SO MUCH!! god bless u! I literally understood the concept in less than a minute. My math exam is next week so I really needed this. (thank you once again!)
your videos are so good crying this is excellent
Thank you!
for sure, I have a Stat201 exam today, and now I got your very amazing video. I'll tell you my exam grade letter. Thank you very much... :)
I hope the exam went well! Thanks so much for watching!
did you pass?
Thank you, Very clear and concise.
You're very welcome - I'm glad it was clear and thanks for watching!
A group of boys at school ABC are doing actuarial science. Each boy takes only Algebra or only Statistics or both Algebra and Statistics. The probability that a boy is taking
Statistics given that he is taking Algebra is 15. The probability that a boy is taking
Algebra given that he is taking Statistics is 13. Find the probability that
A boy selected at random is taking both Statistics and Algebra.
Could you create a video on how to understand what the events would be. how did you know to make those your events in this case.
Kinda beautiful
Thank you!
The probability of playing soccer and playing rugby is 0.32. The probability of playing soccer and not playing rugby is 0.13. What is the probability of playing soccer?
.45
Following you from zambia,
Thank you!
Hieee.... I would like to request make a video on the probability igcse grade 9 problems of conditional probability
Thanks for watching and the request! I don't know much about IGCSE, do you have a link to where I could find these problems? I'll look into it!
Thank you.... It's very kind of you I will send the link
Problems on page 382
25%
what does the "intersection" mean?
The intersection is basically the math version of "and". We may be concerned with the events A and B. Then the event where they BOTH occur would be "A and B", which is the intersection, written A∩B. For example, A may be the event we roll a number less than 5 on a 6-sided die. B may be the event we roll an even number on a 6-sided die. Then, A∩B is the set of events where A and B BOTH occur: { 2, 4 }. Does that help?
Here is a lesson I did on intersections, in the context of set theory: ruclips.net/video/mOMoZYGirQQ/видео.html
It's the same in probability theory, but I am using set language in the lesson as opposed to probability language. For example, an "event" in probability theory is just a set. In particular, it is a subset of the sample space being considered.
@@WrathofMath thank you!!
great video bro
Thank you!
THANKS!
My pleasure, thanks for watching!
Thanks, your videos are really awesome!
Thank you! I'm glad you've found them useful!
You are teaching everything right BUT DO YOU know whats wrong with your tutorial ? You are assuming that people are nerdy and interested to learn probability when the truth is most of them are HERE because they dont understand and that THEY have to learn it as PART of there course .........NOW COMING to the main point .. You skipped showing at 5.36 seconds 2/4 you just directly assumed NOOBS will understand that you reduced 2/4 into 1/2 ....This is the BIGGEST problem with people teaching maths they skip steps thinking the viewer will under stand that where the 1/2 came from .......how ever if you took the time out to say its 2/4 that is reduced to 1/2 aka 0.5 than the NOOBS wont be left wondering how you came to 1/2 .......... I understand to you its COMMON SENSE .. but for the rest of us who are not interested and find maths difficult WE NEED TO see every step ..... ALWAYS teach like you are teaching to a 10 year old .
you got a good point. i am with you here. you shouldnt teach people like they are math experts you should slow down and explain every detail
this channel is targeted for college students if someone doesn't know that 2/4 is 1/2 they must go back to elementary school
@@mohamedtrfnx6632 and that was my actual point you want to TEACH IGNORANTLY not everyone is an Arrogant nerd ... Your teaching method is OLD the new generation requires full information be provided not HALF BAKED tutorials with HALF information and than lazyly saying GO LEARN THE OTHER PART SOMEWHERE ELSE and than come back and watch the tutorial .....
my math teacher got supa angry (furius) when I got these wrong: I hate you😡😎
Where are you from