Bayes/Conditional Probability

While the confusion matrix is easy to understand, it is helpful to get a more general equation to calculate the likelihood of conditional events.

The formula for that is:

P(A|B): Conditional Probability that event A occurs under the condition that B has occurred.

P(B|A):  Conditional Probability that event B occurs under the condition that A has occurred.              

P(A):      Probability that event A occurs.

P(B):      Probability that event B occurs.

Example

Suppose we have three treasure boxes. In each box are two coins. This could be either a silver coin (S) or a gold coin (G). The following list shows how the coins are distributed among the boxes.

Box 1: GG

Box 2: GS

Box 3: SS

If we randomly select a box and draw a gold coin from it blindly, what is the likelihood of selecting box 1?