1. You mentioned you have two exercises: one on conditional probability and one on random variables. 2. Let's start with conditional probability. The problem typically asks: Given two events $A$ and $B$, what is the probability of $A$ occurring given that $B$ has occurred? 3. The formula for conditional probability is: $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ where $P(A \cap B)$ is the probability that both $A$ and $B$ occur, and $P(B)$ is the probability that $B$ occurs. 4. Important rules: - $P(B)$ must be greater than 0. - Conditional probability changes the sample space to event $B$. 5. For the random variable exercise, a random variable is a function that assigns a numerical value to each outcome in a sample space. 6. Common tasks include finding the expected value $E(X)$, variance $Var(X)$, or probability distribution. 7. The expected value is calculated as: $$E(X) = \sum x_i P(X = x_i)$$ where $x_i$ are possible values of $X$. 8. Variance is: $$Var(X) = E[(X - E(X))^2] = E(X^2) - [E(X)]^2$$ 9. If you provide specific problems, I can help solve them step-by-step.