1. **State the problem:** We have a spinner with three colored sections: blue, yellow, and pink. It was spun 100 times. 2. **Given data:** - Frequency of yellow = 45 - Ratio of blue to yellow = 4 : 9 3. **Find:** The estimated probability of landing on pink as a decimal. 4. **Step 1: Find the frequency of blue.** Since the ratio of blue to yellow is 4 : 9 and yellow frequency is 45, we set up the proportion: $$\frac{\text{blue}}{\text{yellow}} = \frac{4}{9}$$ $$\Rightarrow \text{blue} = \frac{4}{9} \times 45 = 20$$ 5. **Step 2: Find the frequency of pink.** Total spins = 100 $$\text{pink} = 100 - (\text{blue} + \text{yellow}) = 100 - (20 + 45) = 35$$ 6. **Step 3: Calculate the probability of pink.** Probability is frequency divided by total spins: $$P(\text{pink}) = \frac{35}{100} = 0.35$$ **Final answer:** The estimated probability of the spinner landing on pink is **0.35**.