1. **State the problem:** A card is drawn from a standard 52-card deck. If the card is a king, you win 30; otherwise, you lose 4. We want to find the expected value $E(X)$ of the amount won in one play. 2. **Formula for expected value:** The expected value of a discrete random variable $X$ is given by: $$E(X) = \sum (x_i \times P(x_i))$$ where $x_i$ are the possible outcomes and $P(x_i)$ their probabilities. 3. **Identify outcomes and probabilities:** - Winning 30 if the card is a king. There are 4 kings in a 52-card deck, so: $$P(\text{king}) = \frac{4}{52} = \frac{1}{13}$$ - Losing 4 if the card is not a king. There are 48 other cards, so: $$P(\text{not king}) = \frac{48}{52} = \frac{12}{13}$$ 4. **Calculate expected value:** $$E(X) = 30 \times \frac{1}{13} + (-4) \times \frac{12}{13}$$ 5. **Simplify:** $$E(X) = \frac{30}{13} - \frac{48}{13} = \frac{30 - 48}{13} = \frac{-18}{13}$$ 6. **Final answer:** $$E(X) = -1.38$$ This means on average, you lose 1.38 per game played.