Question 1: A bag contains 6 red, 4 blue, and 10 green balls. If a ball is drawn at random, what is the relative frequency of drawing a green ball based on this data?

Answer: 10/20 or 0.5

Question 2: In an experiment, a coin is flipped 50 times, and heads occur 28 times. What is the experimental relative frequency of getting heads?

Answer: 28/50 or 0.56

Question 3: A survey recorded 120 students, of which 30 preferred chocolate, 50 preferred vanilla, and the rest preferred strawberry. Calculate the relative frequency of students who preferred strawberry.

Answer: 40/120 or 1/3 ≈ 0.33

Question 4: Plot the graph of y=2x for x values from 0 to 5 on the grid provided.

Answer: See full answer key

Question 5: A die is rolled 60 times. The number 4 appears 8 times. What is the experimental relative frequency of rolling a 4?

Answer: 8/60 or 2/15 ≈ 0.133

Question 6: A spinner has 3 red, 2 yellow, and 5 blue sectors. After 100 spins, red occurs 25 times. What is the relative frequency of landing on red?

Answer: 25/100 or 0.25

Question 7: Construct a triangle on the grid with sides of length 3 cm, 4 cm, and 5 cm, using the scale 1 cm = 1 unit. (Draw on the grid.)

Answer: See full answer key

Question 8: In an experiment, a bag of candies contains 10 red, 20 yellow, and 30 green. A student draws 15 candies and finds 2 red, 5 yellow, and 8 green. Determine the relative frequency of green candies in this sample.

Answer: 8/15 ≈ 0.53

Question 9: A quiz shows that 45 out of 90 students answered a question correctly. What is the relative frequency and what does it suggest about the probability of a student answering correctly?

Answer: 45/90 or 0.5; suggests a 50% chance based on data

Question 10: Identify and correct the mistake in calculating the relative frequency if a student states: 'The relative frequency of blue balls is 8/20, but the total number of balls is 25, so the correct relative frequency is 8/25.'

Answer: The total should include only the relevant data; if total is 20, then 8/20 is correct; if total is 25, then 8/25 is correct only if data shows total is 25.

Question 11: A researcher recorded 200 trials of an experiment and found that the event occurred 45 times. Calculate the relative frequency and interpret its meaning.

Answer: 45/200 or 0.225; meaning the event occurred in 22.5% of trials

Question 12: A survey shows that 60% of people prefer tea over coffee. If 150 people are surveyed, how many preferred tea? What is the relative frequency based on this data?

Answer: 90 people; relative frequency = 0.6