search
Search
Publish
Guest 0reps
Thanks for the thanks!
close
Outline
Cancel
Post
account_circle
Profile
exit_to_app
Sign out
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 Doc Search Code Search Beta SORRY NOTHING FOUND!
mic
Start speaking... Voice search is only supported in Safari and Chrome.
Shrink
Navigate to
A
A
share
thumb_up_alt
bookmark
arrow_backShare Twitter Facebook
thumb_up
0
thumb_down
0
chat_bubble_outline
0
auto_stories new
settings

# Conditional Probability

Probability and Statistics
chevron_right
Probability Theory
schedule Mar 9, 2022
Last updated
local_offer
Tags
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:

$$\mathbb{P}(B|A)=\frac{\mathbb{P}(B\cap{A})}{\mathbb{P}(A)} =\frac{0.2}{0.5} =0.4$$