1. **State the problem:** Yasmin has a bag with 165 colored beads. The table shows the number of beads selected for each color in an experiment where beads are drawn, recorded, and replaced. We want to find which color's experimental probability is closest to the theoretical probability assuming equal numbers of each color in the bag. 2. **Given data:** - Total beads in bag: 165 - Colors and number of beads drawn (experimental counts): - Red: 10 - Brown: 15 - Orange: 17 - Yellow: 13 3. **Theoretical probability:** Since the bag has an equal number of each color, the theoretical probability for each color is $$P_{theoretical} = \frac{1}{4} = 0.25$$ 4. **Experimental probability:** Calculate the experimental probability for each color by dividing the number of beads drawn by the total beads drawn (sum of experimental counts): $$\text{Total drawn} = 10 + 15 + 17 + 13 = 55$$ - Red: $$P_{red} = \frac{10}{55} = \frac{2}{11} \approx 0.1818$$ - Brown: $$P_{brown} = \frac{15}{55} = \frac{3}{11} \approx 0.2727$$ - Orange: $$P_{orange} = \frac{17}{55} \approx 0.3091$$ - Yellow: $$P_{yellow} = \frac{13}{55} \approx 0.2364$$ 5. **Compare experimental to theoretical probabilities:** - Red difference: $$|0.1818 - 0.25| = 0.0682$$ - Brown difference: $$|0.2727 - 0.25| = 0.0227$$ - Orange difference: $$|0.3091 - 0.25| = 0.0591$$ - Yellow difference: $$|0.2364 - 0.25| = 0.0136$$ The experimental probability closest to the theoretical probability is for **Yellow** beads. 6. **Estimate number of beads of each color in the bag:** Since total beads are 165 and the bag is assumed to have equal numbers of each color, $$\text{Number of beads per color} = \frac{165}{4} = 41.25$$ Since beads must be whole numbers, approximately 41 beads of each color are in the bag. **Final answers:** - Color with experimental probability closest to theoretical: **Yellow** - Estimated number of beads of each color: **41**