Question

cathy conducted an experiment in which she placed red, yellow, blue, and orange pieces of paper in a hat and drew them out without looking. the number of times cathy drew each color is shown in the table below. based on her experiment, what is the probability that the next slip of paper cathy draws will be red?
a) \\(\frac{1}{33}\\) b) \\(\frac{2}{9}\\) c) \\(\frac{1}{5}\\) d) \\(\frac{2}{11}\\)

colors cathy drew	color	frequency
	yellow	5
	blue	12
	orange	28

Explanation:

Step1: Calculate total number of draws

Sum the frequencies: \(10 + 5 + 12 + 28 = 55\)

Step2: Calculate probability of red

Probability is red frequency over total: \(\frac{10}{55}=\frac{2}{11}\)? Wait, no, wait. Wait, 10 (red) +5 (yellow)+12 (blue)+28 (orange) = 10+5=15, 15+12=27, 27+28=55. Wait, but the options: A is 1/55, B is 2/9, C is 1/5, D is 2/11? Wait, no, 10/55 simplifies to 2/11? Wait, 10 divided by 55: divide numerator and denominator by 5, 2/11. Wait, but let's check again. Wait, the table: Red:10, Yellow:5, Blue:12, Orange:28. Total trials: 10+5+12+28=55. So probability of red is number of red draws over total draws, which is 10/55 = 2/11? Wait, but option D is 2/11. Wait, but let me check the options again. The options are A:1/55, B:2/9, C:1/5, D:2/11. So 10/55 simplifies to 2/11 (divide numerator and denominator by 5: 10÷5=2, 55÷5=11). So the probability is 2/11.

Answer:

D. \(\frac{2}{11}\)