Final answer:
In a decision-making problem with 36 possible outcomes and 9 states of nature, the number of decision alternatives is calculated by dividing the total number of outcomes by the number of states of nature, resulting in 4 decision alternatives.
Step-by-step explanation:
In a decision-making problem with 36 possible outcomes and 9 states of nature, the number of decision alternatives is determined by how many choices or actions can be taken in each state of nature. Since there are 36 outcomes that must be accounted for by the combination of states of nature and decision alternatives, we can deduce that each state of nature is paired with a specific set of decision alternatives to cover all possible outcomes.
If we consider that the 36 possible outcomes are the result of all combinations between states of nature and decision alternatives, we divide the total number of outcomes by the number of states of nature to find the number of decision alternatives. Therefore, the number of decision alternatives is 36 outcomes divided by 9 states of nature, yielding 4 decision alternatives.