Final answer:
In a pure exchange economy, the probability of state a occurring is 2/3.
Step-by-step explanation:
In this pure exchange economy, there are two states of the world, a and b, where state a occurs with a probability of 2/3 and state b occurs with a probability of 1/3. The probability of an event happening is calculated by dividing the number of desired outcomes by the total number of possible outcomes. In this case, there are two possible outcomes (states a and b) and state a occurs 2 out of 3 times, so the probability that state a occurs is 2/3.