1. The problem is to understand and calculate the conditional probabilities $P(X_2|C_1)$ and $P(X_2|C_2)$. 2. Conditional probability $P(A|B)$ is defined as the probability of event $A$ occurring given that event $B$ has occurred, and is calculated by the formula: $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ where $P(A \cap B)$ is the probability of both $A$ and $B$ happening, and $P(B)$ is the probability of $B$. 3. To find $P(X_2|C_1)$, you need the joint probability $P(X_2 \cap C_1)$ and the probability $P(C_1)$. 4. Similarly, to find $P(X_2|C_2)$, you need $P(X_2 \cap C_2)$ and $P(C_2)$. 5. Without specific values or distributions for $X_2$, $C_1$, and $C_2$, the exact numerical probabilities cannot be computed. 6. If you have data or probability distributions, plug those into the formula above to calculate the conditional probabilities. 7. Remember, these probabilities help understand how likely $X_2$ is under the conditions $C_1$ or $C_2$, which is useful in classification or decision-making problems.