If we have an event or scenario S, the event not-S, called the complement of S, is written SC. Note that P(S) + P(SC) = 1, as either S or not-S must occur.
The total probability rule explains the unconditional probability of an event in terms of probabilities conditional on the scenarios.
Suppose there are two events:
The probability of an increase in IBM's revenue given an economic expansion is P(A|B) = 0.8.
Using the total probability rule, we can compute the probability of an increase in IBM's revenue: P(A) = P(A|B) x P(B) + P(A|Bc) x P(Bc) = 0.8 x 0.6 + 0.7 x 0.4 = 0.76.
Typical exam question
An analyst constructs the following probability table for the market and Company X's stock:
1. Compute the total probability of good performance for Company X's stock.
Here we are asked to find the total probability of good performance. This means we have to find the joint probability of one stock outcome. To do this we multiply and add.
We take Σ (probability of economic state x good conditional probability): Joint probability = (0.5 x 0.4) + (0.3 x 0.5) + (0.2 x 0.5) = 45%
2. Compute the probability of simultaneously realizing a bull economy and poor stock performance for Company X.
This question asks you to determine the probability of a specific branch. If we follow the branch and multiply the probabilities, we will arrive at the correct answer as follows.
Bull economy: 0.5
|jackwez: an easy way to remember this is the fact that A|B is like A/B multipled by B equals A.... along the same lines as teh dupont questions...|
|wundac: thanks jack|
|mdejesus: Man... I can't remember these formulas at all. But I CAN make a mean tree diagram. Making a tree diagram seems to be more helpful for me :)|
|choas69: but u cant keep making trees in an exam bro|
|gyee2012: Realize the change in mutliplication between independent and dependent probability and you will be set|