Question

the frequency table shows the results of drawing 20 cards from a bag of 100. there are an equal number of cards of each color in the bag. which color has the same frequency as the distribution of colors in the bag?
color\tfrequency
blue\t4
red\t3
white\t5
yellow\t8
white
red
blue
yellow

Explanation:

Step1: Determine the expected frequency per color in the bag.

Since there are an equal number of cards of each color in the bag of 100, and there are 4 colors (Blue, Red, White, Yellow), the expected number of cards per color in the bag is $\frac{100}{4} = 25$. But we are looking at the frequency in a sample of 20 draws. The expected frequency in the sample for a color with equal distribution in the bag would be proportional. Since the bag has equal numbers, the probability of each color is $\frac{1}{4}$. So the expected frequency in 20 draws is $20\times\frac{1}{4}=5$.

Step2: Compare the sample frequencies to the expected frequency.

• Blue: 4 (not 5)
• Red: 3 (not 5)
• White: 5 (matches the expected frequency of 5)
• Yellow: 8 (not 5)

Answer:

white