Answer: 0.1

## Explanation The joint probability matrix must sum to 1 (or 100%) since it represents all possible outcomes. The given probabilities are: - Good economy with interest rate increase: 20% - Good economy with no interest rate increase: 10% - Normal economy with interest rate increase: 30% - Normal economy with no interest rate increase: 20% - Poor economy with no interest rate increase: 10% - Poor economy with interest rate increase: X (unknown) Sum of all known probabilities = 20% + 10% + 30% + 20% + 10% = 90% Therefore, X = 100% - 90% = 10% So the joint probability of a poor economy and an increase in interest rate is 10% or 0.1. This is a basic probability concept where the sum of all joint probabilities in a complete probability space must equal 1.

Author: Nikitesh Somanthe