The total probability rule explains the unconditional probability of an event in terms of probabilities conditional on the scenarios.
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
Poor stock: 0.3
Probability = 0.5 x 0.3 = 0.15 = 15%