What's the probability of something happening if something else has already happened? This type of probability is called conditional probability.
If you are trying to determine the probability that event B will occur, given that another event (A) has already occurred, it is written with the following notation:
P(B, given A) = P(B | A)
This is the notation of the probability that event B occurs, given event A has also occurred -- the vertical bar is pronounced "given".
Conditional probability is calculated with the following formula:
The probability that event B occurs, given that event A also occurs, is the probability of both A and B occurring divided by the probability of event A.
EXAMPLE
Suppose you are rolling a standard six-sided die. What is the probability of rolling a 4?A Venn diagram is a useful tool to visualize conditional probability.
EXAMPLE
What is the probability of getting an even on a roulette wheel? Like the example above, this question is not a conditional probability yet because the question is simply about the probability that the number is even. To find the answer, count up all of the even sectors.Source: Adapted from Sophia tutorial by Jonathan Osters.