Intro to Conditional Probability | Probability Theory
27.2 هزار بار بازدید -
5 سال پیش
-
What is conditional probability? How
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 YouTube 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: https://amzn.to/2Z8MrB7
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtu...
Vallow SoundCloud: SoundCloud: benwatts-3
********************************************************************
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: Patreon: wrathofmathlessons
Follow Wrath of Math on...
● Instagram: Instagram: wrathofmathedu
● Facebook: Facebook: WrathofMath
● Twitter: Twitter: wrathofmathedu
My Music Channel: seanemusic
Here’s an example of conditional probability: the probability that a YouTube 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: https://amzn.to/2Z8MrB7
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtu...
Vallow SoundCloud: SoundCloud: benwatts-3
********************************************************************
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: Patreon: wrathofmathlessons
Follow Wrath of Math on...
● Instagram: Instagram: wrathofmathedu
● Facebook: Facebook: WrathofMath
● Twitter: Twitter: wrathofmathedu
My Music Channel: seanemusic
5 سال پیش
در تاریخ 1398/05/24 منتشر شده
است.
27,280
بـار بازدید شده