Meaning & use
conditional probability
Last updated
Meaning
nouncountable or uncountabletechnicalmathematics
The probability that one event happens, calculated knowing that another event has already happened.
Grammar: Often used with 'the' or 'a'; can be uncountable when referring to the concept in general.
Patterns
- conditional probability of something
- conditional probability that ...
- conditional probability given something
The conditional probability of drawing a red card, given that the first card was black, is about 0.51.
In medical testing, the conditional probability of a positive result given that the patient has the disease is called sensitivity.
She explained that conditional probability is not the same as the probability of both events happening together.
Common combinations
- conditional probability distribution
- The conditional probability distribution of Y given X is central to regression analysis.
- calculate conditional probability
- You can calculate conditional probability using Bayes' theorem.
- conditional probability formula
- The conditional probability formula is P(A|B) = P(An and B) / P(B).
- conditional probability of an event
- The conditional probability of an event can change dramatically when new information arrives.
Word family
- condition noun
- A situation that must exist before something else can happen.
- conditional adjective
- Depending on something else; not absolute.
- probability noun
- A measure of how likely an event is.
Commonly confused: conditional probability or joint probability?
conditional probability vs joint probability
Joint probability is the chance of two events happening together, while conditional probability is the chance of one event given that the other has happened.
Practice
If P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2, what is the conditional probability P(A|B)?
Choose one answer.
P(A|B) = P(An and B) / P(B) = 0.2 / 0.4 = 0.5. The other options are either the joint probability or the individual probabilities, not the conditional one.
Make it your own
Write a sentence using “conditional probability”, then check it and compare it with the examples above.