Conditional probability - Revision history

DavidB4-bot: clean up & uniformity

2016-07-13T06:42:08Z

clean up & uniformity

GregG: clarify notation

2012-05-06T20:15:34Z

clarify notation

Foxtrot: math and wikilinks

2008-05-12T00:12:13Z

math and wikilinks

Henry8th: 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 ...

2008-05-11T22:38:56Z

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 ...

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 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]]

@@ Line 7: / Line 7: @@
 where P(AB) is the probability of both events A and B occurring and P(B) is the probability of event B occurring.
-===Example===
+==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.
@@ Line 21: / Line 21: @@
 In the second case, the question requires a conditional probability: P(red on 2nd draw|red on 1st draw).
-===See also===
+==See also==
 [[Bayes theorem]]
 [[Category:Probability and Statistics]]

@@ Line 19: / Line 19: @@
 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).
+In the second case, the question requires a conditional probability: P(red on 2nd draw|red on 1st draw).
 ===See also===

@@ Line 2: / Line 2: @@
 <math>
-P(A|B)=P(AB)/P(B)
+P(A|B)=\frac{P(AB)}{P(B)}
 </math>
@@ Line 22: / Line 22: @@
 ===See also===
-[[Bayes'_theorem]]
+[[Bayes theorem]]
 [[Category:Probability and Statistics]]