1. **State the problem:** We have a total of 19 items in the universal set $\xi$. Sets $M$ and $N$ are subsets of $\xi$ with the following counts: - $8$ items in $M$ only - $2$ items in both $M$ and $N$ - $4$ items in $N$ only - $5$ items outside both $M$ and $N$ We want to find the probability that a randomly chosen item is in $M' \cap N$, which means the item is **not in $M$ but in $N$**. 2. **Recall the formula:** The probability of an event $A$ is given by $$\text{P}(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 3. **Identify the favorable outcomes:** The set $M' \cap N$ includes items that are in $N$ but not in $M$. From the diagram, these are the items in $N$ only, which is $4$. 4. **Calculate the probability:** $$\text{P}(M' \cap N) = \frac{4}{19}$$ 5. **Final answer:** The probability that an item chosen at random is in $M' \cap N$ is $$\boxed{\frac{4}{19}}$$