Question

a bag contains 1 red tile, 1 blue tile, 1 green tile, 1 yellow tile, and 1 purple tile. kaison chooses a tile from the bag, records its color, and then replaces the tile. she repeats this procedure a total of 50 times. her results are shown in the table.

table:
color | observed frequency | relative frequency
red | 15 | \\(\frac{3}{10}\\)
blue | 12 | \\(\frac{6}{25}\\)
green | 8 | \\(\frac{4}{25}\\)
yellow| 10 | \\(\frac{1}{5}\\)
purple| 5 | \\(\frac{1}{10}\\)

Explanation:

Since the problem isn't fully clear (maybe verifying relative frequencies or something else), let's check the total number of trials first. The observed frequencies are 15 (Red) + 12 (Blue) + 8 (Green) + 10 (Yellow) + 5 (Purple) = 15 + 12 = 27; 27 + 8 = 35; 35 + 10 = 45; 45 + 5 = 50. So total trials are 50, which matches the problem statement (50 times). Now, let's check relative frequencies:

• Red: \( \frac{15}{50} = \frac{3}{10} \) (matches the table)
• Blue: \( \frac{12}{50} = \frac{6}{25} \) (matches)
• Green: \( \frac{8}{50} = \frac{4}{25} \) (matches)
• Yellow: \( \frac{10}{50} = \frac{1}{5} \) (matches)
• Purple: \( \frac{5}{50} = \frac{1}{10} \) (matches)

So all relative frequencies are correctly calculated as observed frequency divided by total trials (50). If the question was to verify or calculate relative frequencies, this is the check.

Step1: Calculate total trials

Sum observed frequencies: \( 15 + 12 + 8 + 10 + 5 = 50 \)

Step2: Check each relative frequency

• Red: \( \frac{15}{50} = \frac{3}{10} \) (matches)
• Blue: \( \frac{12}{50} = \frac{6}{25} \) (matches)
• Green: \( \frac{8}{50} = \frac{4}{25} \) (matches)
• Yellow: \( \frac{10}{50} = \frac{1}{5} \) (matches)
• Purple: \( \frac{5}{50} = \frac{1}{10} \) (matches)

Answer:

All relative frequencies are correctly calculated (observed frequency / 50), matching the table.