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Experimental Probability

Grade 7 · Statistics · Worksheet 3

  1. Kaia rolled a standard six-sided die 175 times. The number 3 appeared 31 times. Approximate P(3) as a decimal rounded to the nearest hundredth. Answer: ______________
  2. Mason rolled a standard six-sided die 200 times and recorded the number 5 appearing 39 times. Approximate P(5). Answer: ______________
  3. Emma rolled a standard six-sided die 175 times. She recorded the number 3 appearing 31 times. Approximate P(3). Answer: ______________
  4. Mason is conducting a probability experiment by rolling a standard six-sided die. He rolls the die 12,000 times and records that he rolls a number greater than 4 (i.e., a 5 or a 6) exactly 3,972 times. Based on his experimental data, what is the experimental probability of rolling a number greater than 4? Express your answer as a decimal rounded to the nearest thousandth. Answer: ______________
  5. Matiu rolled a standard six-sided die 120 times. He recorded the number 4 appearing 18 times. Approximate P(4). Answer: ______________
  6. A school is conducting a survey about favorite school subjects. They randomly select 120 students from the 7th grade population of 400 students. In the sample, 45 students said math was their favorite subject. Based on this sample, approximately how many students in the entire 7th grade would you expect to have math as their favorite subject? Answer: ______________
  7. Mere is conducting a probability experiment using a spinner divided into 7 equal-sized sections, each labeled with a different letter: A, B, C, D, E, F, and G. She spins the spinner 14,000 times and records the results. The bar graph from her experiment shows the following frequencies: A: 2,050 times B: 1,980 times C: 2,020 times D: 1,990 times E: 2,010 times F: 1,970 times G: 1,980 times Based on Mere's experimental data, what is the approximate probability that the spinner will land on a vowel (A or E)? Express your answer as a decimal rounded to the nearest thousandth. Answer: ______________
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Answer Key & Explanations

Experimental Probability · Grade 7 · Worksheet 3

  1. Kaia rolled a standard six-sided die 175 times. The number 3 appeared 31 times. Approximate P(3) as a decimal rounded to the nearest hundredth. Answer: 0.18 Solution: Identify the number of times the event occurred: 31 times. Identify the total number of trials: 175 rolls. Calculate the relative frequency: 31 ÷ 175 = 0.177142857...
    Full step-by-step solution

    Step 1: Identify the number of times the event occurred: 31 times. Step 2: Identify the total number of trials: 175 rolls. Step 3: Calculate the relative frequency: 31 ÷ 175 = 0.177142857... Step 4: Round to the nearest hundredth: Look at the thousandths digit (7). Since 7 ≥ 5, round the hundredths digit up from 7 to 8. So 0.177... rounds to 0.18. The approximate probability P(3) is 0.18.

  2. Mason rolled a standard six-sided die 200 times and recorded the number 5 appearing 39 times. Approximate P(5). Answer: 0.195 Solution: Identify the number of times the event (rolling a 5) occurred: 39. Identify the total number of trials: 200.
    Full step-by-step solution

    Step 1: Identify the number of times the event (rolling a 5) occurred: 39. Step 2: Identify the total number of trials: 200. Step 3: Experimental probability (relative frequency) = number of successful outcomes / total number of trials = 39 / 200. Step 4: Convert the fraction to a decimal: 39 ÷ 200 = 0.195. The approximate probability of rolling a 5 based on this experiment is 0.195.

  3. Emma rolled a standard six-sided die 175 times. She recorded the number 3 appearing 31 times. Approximate P(3). Answer: 0.1771 Solution: Identify the number of times the event occurred: 31 times. Identify the total number of trials: 175 rolls. Calculate the relative frequency: 31 ÷ 175 = 0.177142857...
    Full step-by-step solution

    Step 1: Identify the number of times the event occurred: 31 times. Step 2: Identify the total number of trials: 175 rolls. Step 3: Calculate the relative frequency: 31 ÷ 175 = 0.177142857... Step 4: Round to four decimal places: 0.1771. The approximate probability P(3) is 0.1771.

  4. Mason is conducting a probability experiment by rolling a standard six-sided die. He rolls the die 12,000 times and records that he rolls a number greater than 4 (i.e., a 5 or a 6) exactly 3,972 times. Based on his experimental data, what is the experimental probability of rolling a number greater than 4? Express your answer as a decimal rounded to the nearest thousandth. Answer: 0.331 Solution: Identify the number of successful outcomes. Rolling a number greater than 4 (5 or 6) occurred 3,972 times. Identify the total number of trials.
    Full step-by-step solution

    Step 1: Identify the number of successful outcomes. Rolling a number greater than 4 (5 or 6) occurred 3,972 times. Step 2: Identify the total number of trials. Mason rolled the die 12,000 times. Step 3: Calculate the experimental probability: successful outcomes / total trials = 3,972 / 12,000. Step 4: Perform the division: 3,972 ÷ 12,000 = 0.331. Step 5: Round to the nearest thousandth. The decimal is already 0.331, so no rounding is needed. Therefore, the experimental probability of rolling a number greater than 4 is 0.331.

  5. Matiu rolled a standard six-sided die 120 times. He recorded the number 4 appearing 18 times. Approximate P(4). Answer: 0.15 Solution: Identify the number of times the event occurred: 18 times. Identify the total number of trials: 120 rolls. Calculate the relative frequency: 18 ÷ 120 = 0.15.
    Full step-by-step solution

    Step 1: Identify the number of times the event occurred: 18 times. Step 2: Identify the total number of trials: 120 rolls. Step 3: Calculate the relative frequency: 18 ÷ 120 = 0.15. Step 4: The approximate probability P(4) is 0.15. The answer is 0.15.

  6. A school is conducting a survey about favorite school subjects. They randomly select 120 students from the 7th grade population of 400 students. In the sample, 45 students said math was their favorite subject. Based on this sample, approximately how many students in the entire 7th grade would you expect to have math as their favorite subject? Answer: 150 Solution: We have a sample of 120 students from a total of 400 students. In the sample, 45 students said math was their favorite subject.
    Full step-by-step solution

    Step 1: Understand the problem. We have a sample of 120 students from a total of 400 students. In the sample, 45 students said math was their favorite subject. We want to estimate how many of the total 400 students would say math is their favorite subject. Step 2: Find the proportion in the sample. The proportion of students in the sample who like math is: 45 / 120 Step 3: Simplify the fraction. 45/120 = (45 ÷ 15) / (120 ÷ 15) = 3/8 So, 3 out of every 8 students in the sample like math. Step 4: Apply the proportion to the whole population. If the same proportion holds for the entire 7th grade, then the expected number of students who like math in the whole population is: (3/8) × 400 Step 5: Perform the multiplication. (3/8) × 400 = (3 × 400) / 8 = 1200 / 8 = 150 Step 6: Conclusion. Based on the sample, we would expect about 150 students in the entire 7th grade to have math as their favorite subject.

  7. Mere is conducting a probability experiment using a spinner divided into 7 equal-sized sections, each labeled with a different letter: A, B, C, D, E, F, and G. She spins the spinner 14,000 times and records the results. The bar graph from her experiment shows the following frequencies: A: 2,050 times B: 1,980 times C: 2,020 times D: 1,990 times E: 2,010 times F: 1,970 times G: 1,980 times Based on Mere's experimental data, what is the approximate probability that the spinner will land on a vowel (A or E)? Express your answer as a decimal rounded to the nearest thousandth. Answer: 0.290 Solution: Identify the vowels from the letters A, B, C, D, E, F, G. The vowels are A and E. A: 2,050 times E: 2,010 times Add the frequencies: 2,050 + 2,010 = 4,060 times.
    Full step-by-step solution

    Step 1: Identify the vowels from the letters A, B, C, D, E, F, G. The vowels are A and E. Step 2: Find the frequencies for A and E from the data: A: 2,050 times E: 2,010 times Step 3: Add the frequencies: 2,050 + 2,010 = 4,060 times. Step 4: Total number of spins = 14,000. Step 5: Experimental probability = 4,060 / 14,000 = 0.29. Step 6: Round to the nearest thousandth: 0.290. The answer is 0.290.