search
Search
Publish
menu
menu search toc more_vert
Robocat
Guest 0reps
Thanks for the thanks!
close
Outline
Comments
Log in or sign up
Cancel
Post
account_circle
Profile
exit_to_app
Sign out
help Ask a question
Share on Twitter
search
keyboard_voice
close
Searching Tips
Search for a recipe: "Creating a table in MySQL"
Search for an API documentation: "@append"
Search for code: "!dataframe"
Apply a tag filter: "#python"
Useful Shortcuts
/ to open search panel
Esc to close search panel
to navigate between search results
d to clear all current filters
Enter to expand content preview
icon_star
Doc Search
icon_star
Code Search Beta
SORRY NOTHING FOUND!
mic
Start speaking...
Voice search is only supported in Safari and Chrome.
Navigate to
A
A
share
thumb_up_alt
bookmark
arrow_backShare
Twitter
Facebook

Conditional Probability

Probability and Statistics
chevron_right
Probability Theory
schedule Mar 9, 2022
Last updated
local_offer
Tags
tocTable of Contents
expand_more

Let $A$ and $B$ be any two mutually exclusive events defined over $S$. Then the following is true:

$$\mathbb{P}(B|A)=\frac{\mathbb{P}(B\cap{A})}{\mathbb{P}(A)}$$

$\mathbb{P}(B|A)$ is read as the "probability of $B$ given that $A$ occurred".

Example

Question. The probability that a product is defective is 0.5. The probability that a product is defective and a customer complains is 0.2. What is the probability that a customer complains given that the product is defective?

Solution. Let A be the event that the product is defective. Let B denote the event that a customer complains. Then probability that a customer complains given that the product is defective is:

$$\mathbb{P}(B|A)=\frac{\mathbb{P}(B\cap{A})}{\mathbb{P}(A)} =\frac{0.2}{0.5} =0.4$$
robocat
Published by Isshin Inada
Edited by 0 others
Did you find this page useful?
thumb_up
thumb_down
Ask a question or leave a feedback...
thumb_up
0
thumb_down
0
chat_bubble_outline
0
settings
A modern learning experience for data science and analytics