Question

In the given decision situation with three possible states of nature (s1, s2, and s3) and the specified prior probabilities, what is the sum of the prior probabilities of all the states of nature?

(a) 0.1
(b) 0.5
(c) 0.4
(d) 1.0

Answer 1

The sum of the prior probabilities of all states of nature in a decision situation must equal 1, so the correct answer is (d) 1.0, which represents 100% of the sample space.

Step-by-step explanation:

The sum of the prior probabilities of all states of nature (s1, s2, and s3) in any decision situation must always equal 1. This is a fundamental rule of probability distributions. The prior probability represents the probability of each state occurring before taking into account any new information. Since there is no new information that affects the probabilities of the states of nature, the sum of these probabilities is the total probability of all possible outcomes.

Therefore, the correct answer is (d) 1.0. This is because the sum of all prior probabilities in a probability distribution must always add up to 1, representing 100 percent of the sample space, as indicated in the example solutions given for related probability problems.