IDEA FOUND // IDEA 143
Conditional Probability
“A new condition changes the universe of cases you are counting over.”
01 / PLAINLY
What it means, plainly
Conditional probability asks about A only among cases where B occurred. It is written P(A|B) and read ‘the probability of A given B.’
02 / CONTEXT
A little more
P(A|B) is the probability of A restricted to situations where B occurred, provided P(B) is positive. It usually differs from P(A) and is not interchangeable with P(B|A).
03 / WHY IT MATTERS
Why it matters
It prevents two questions with different reference groups from being mixed, especially when a condition adds new information.
04 / EXAMPLE
A familiar example
The probability of rain given overcast skies is not the probability of overcast skies given rain.
05 / LIMIT
What it does not mean
Reversing the condition is a common error, especially when interpreting diagnostic tests.
06 / NOTICE
Notice it in your day
Write two different questions using rain and overcast skies: P(rain|overcast) and P(overcast|rain). Describe which days you would count in each.
FINAL NOTE
The idea worth keeping
Read the bar as given that and name the new reference universe first.
QUESTIONS / 02
Questions people still have
How do you read P(A|B)?
It is the probability of A given that B occurred, using those cases as the reference set.
Is P(A|B) the same as P(B|A)?
Not necessarily. Each expression restricts the calculation to a different set of cases.