Decide which method (theoretical or relative frequency) is appropriate, and compute or estimate the probability of the following event. Randomly selecting a yellow tie from a drawer that holds nine blue ties, three red ties, and eleven yellow ties Decide which method (theoretical or relative frequency) is appropriate. Choose the correct answer below. The theoretical method should be used because all outcomes are not equally likely. B. The relative frequency method should be used because there is data from many observations. $x$. The relative frequency method should be used because there is no data from observations. * The theoretical method should be used because all outcomes are equally likely. Compute or estimate the probability of selecting a yellow tie. $\square$ (Type an integer or a simplified fraction.)
Solution
Step 1 ：Decide which method (theoretical or relative frequency) is appropriate. The correct answer is the theoretical method should be used because all outcomes are equally likely.
Step 2 ：Compute the probability of selecting a yellow tie. The number of yellow ties is 11 and the total number of ties is 23 (9 blue ties, 3 red ties, and 11 yellow ties).
Step 3 ：Calculate the probability by dividing the number of yellow ties by the total number of ties. The probability is \( \frac{11}{23} \approx 0.478 \).
Step 4 ：The probability of selecting a yellow tie from the drawer is approximately 0.478, or 47.8%. This means that if we were to randomly select a tie from the drawer, there is a 47.8% chance that it would be yellow.
Step 5 ：Final Answer: The probability of selecting a yellow tie is approximately \(\boxed{0.478}\) or \(\boxed{47.8\%}\).
