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New page: A '''conditional probability''' is the probability that some event A occurs given that a different event B has already occurred. This is written P(A|B) (often read as "the probability ...
A '''conditional probability''' is the [[probability]] that some event A occurs given that a different event B has already occurred. This is written P(A|B) (often read as "the probability of A given B"). The conditional probability satisfies the equation
<math>
P(A|B)=P(AB)/P(B)
</math>
where P(AB) is the probability of both events A and B occurring and P(B) is the probability of event B occurring.
===Example===
A bag has 5 red balls and 3 green balls inside it. You pick out a ball and do not replace it in the bag afterwards.
Q. What is the probability of removing a red ball?
A. 5/8
Q. What is the probability of removing a red ball, ''given that you have already removed a red ball''?
A. There are now 4 red balls and 3 greens, so: 4/7
In the second case, the question requires a conditional probability: P(red|red).
===See also===
[[Bayes'_theorem]]
[[Category:Probability and Statistics]]
<math>
P(A|B)=P(AB)/P(B)
</math>
where P(AB) is the probability of both events A and B occurring and P(B) is the probability of event B occurring.
===Example===
A bag has 5 red balls and 3 green balls inside it. You pick out a ball and do not replace it in the bag afterwards.
Q. What is the probability of removing a red ball?
A. 5/8
Q. What is the probability of removing a red ball, ''given that you have already removed a red ball''?
A. There are now 4 red balls and 3 greens, so: 4/7
In the second case, the question requires a conditional probability: P(red|red).
===See also===
[[Bayes'_theorem]]
[[Category:Probability and Statistics]]