1. **State the problem:** We have data from trials involving drawing cards labeled 1, 2, 3, 4 and flipping a coin (Heads or Tails). We want to find the experimental probability and theoretical probability of the event: drawing a 2, 3, or 4 card and flipping heads in a single trial. 2. **Experimental probability:** This is calculated as the number of favorable outcomes divided by the total number of trials. - Favorable outcomes are trials where the card is 2H, 3H, or 4H. - From the data: 2H = 14, 3H = 20, 4H = 15. - Total favorable outcomes = $14 + 20 + 15 = 49$. - Total trials = sum of all trials = $13 + 14 + 20 + 15 + 13 + 11 + 18 + 16 = 120$. - Experimental probability = $\frac{49}{120} \approx 0.408$ (rounded to nearest thousandth). 3. **Theoretical probability:** Assuming the card is chosen at random and the coin is fair. - Probability of drawing a 2, 3, or 4 card = $\frac{3}{4}$ (since 4 cards total, 3 favorable). - Probability of flipping heads = $\frac{1}{2}$. - Since these are independent events, multiply probabilities: $$P = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} = 0.375$$ - Rounded to nearest thousandth: 0.375. **Final answers:** - Experimental probability = 0.408 - Theoretical probability = 0.375