Final answer:
The total number of possible outcomes in a decision-making problem with 4 decision alternatives and 5 states of nature is 20, calculated by multiplying the decision alternatives by the states of nature.
Step-by-step explanation:
In a decision-making problem with 4 decision alternatives and 5 states of nature, to find the total number of possible outcomes, you would multiply the number of decision alternatives by the number of states of nature. Each alternative can result in one of the states of nature, so for 4 decision alternatives and 5 states of nature, you would have:
4 (decision alternatives) × 5 (states of nature) = 20 possible outcomes.
This can be considered as having a set of 4 options for each of the 5 scenarios, leading to a total outcome calculation of 4 × 5. It is important to acknowledge that this calculation assumes each decision alternative can occur with each state of nature.