Calculates the probability of one event happening given that another does. The given event could have been a consequence of either of two alternative sources which are independent of each other.
| P(A1 given B) is equal to |
| P(A1) x P(B given A1) |
| -------------------------------------------------------------------- |
| [P(A1) x P(B given A1)] + [P(A2) x P(B given A2)] |
where A1 and A2 are the only two ways that B can occur.
For example, aces are 8/48 of the cards in a pinochle deck but only 4/52 in a poker deck. If you have a deck of each kind, what is the probability that a poker deck was drawn from given that an ace was picked?
| Answer: | P(ACE given POKER)=1/13 |
| P(ACE given PINOCHLE)=1/6 | |
| (1/13) / (1/13 + 1/6) = 6/19. |