1. **State the problem:** We need to find the mean (expected value) of the random variable $X$, which represents the number of packs Rodrigo buys until he gets his favorite card. 2. **Recall the formula for the mean of a discrete random variable:** $$\mu_X = E(X) = \sum x_i P(X = x_i)$$ where $x_i$ are the values of $X$ and $P(X = x_i)$ are their probabilities. 3. **Given values:** - $X = 1, 2, 3$ - $P(X=1) = 0.10$ - $P(X=2) = 0.09$ - $P(X=3) = 0.81$ 4. **Calculate the mean:** $$\mu_X = 1 \times 0.10 + 2 \times 0.09 + 3 \times 0.81$$ $$= 0.10 + 0.18 + 2.43$$ $$= 2.71$$ 5. **Interpretation:** On average, Rodrigo will buy about 2.71 packs to get his favorite card. **Final answer:** $$\mu_X = 2.71 \text{ packs}$$