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Experimental Probability

Grade 7 · Statistics · Worksheet 1

  1. Mason rolled a standard six-sided die 200 times and recorded the number 5 appearing 39 times. Approximate P(5). Answer: ______________
  2. Emma is testing a new game that uses a spinner divided into 4 equal sections: red, blue, yellow, and green. She spins the spinner 500 times and records the results in a bar graph. The bar for red has a height of 135, the bar for blue has a height of 120, the bar for yellow has a height of 145, and the bar for green has a height of 100. Based on Emma's experimental data, what is the approximate probability that the spinner will land on red or green? Express your answer as a decimal rounded to the nearest hundredth. Answer: ______________
  3. Tane rolled a standard six-sided die 135 times. He recorded the number 3 appearing 27 times. Approximate P(3). Answer: ______________
  4. Noah is testing a new board game that uses a spinner divided into 4 equal sections labeled A, B, C, and D. He spins the spinner 500 times and records the results. The table below shows how many times each letter appeared: A: 132 times B: 118 times C: 127 times D: 123 times Based on Noah's experimental data, what is the approximate probability that the spinner will land on a letter that comes before C in the alphabet? Express your answer as a decimal rounded to the nearest hundredth. Answer: ______________
  5. Mere is conducting a probability experiment by flipping a fair coin. She flips the coin 8,000 times and records that it lands on heads 4,128 times. Based on her experimental data, what is the approximate experimental probability of flipping heads? Express your answer as a decimal rounded to the nearest thousandth. Answer: ______________
  6. Emma rolled a standard six-sided die 80 times. She recorded the number 5 appearing 15 times. Approximate P(5). Answer: ______________
  7. A school is conducting a survey about favorite school subjects. In a random sample of 200 students, 45 students chose mathematics as their favorite subject. Based on this sample, approximately how many students would you expect to choose mathematics as their favorite subject if the entire school has 1,240 students? Answer: ______________
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Answer Key & Explanations

Experimental Probability · Grade 7 · Worksheet 1

  1. 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.

  2. Emma is testing a new game that uses a spinner divided into 4 equal sections: red, blue, yellow, and green. She spins the spinner 500 times and records the results in a bar graph. The bar for red has a height of 135, the bar for blue has a height of 120, the bar for yellow has a height of 145, and the bar for green has a height of 100. Based on Emma's experimental data, what is the approximate probability that the spinner will land on red or green? Express your answer as a decimal rounded to the nearest hundredth. Answer: 0.47 Solution: Identify outcomes for red or green: red appeared 135 times, green appeared 100 times. Add their frequencies: 135 + 100 = 235 times. Total number of spins = 500.
    Full step-by-step solution

    Step 1: Identify outcomes for red or green: red appeared 135 times, green appeared 100 times. Step 2: Add their frequencies: 135 + 100 = 235 times. Step 3: Total number of spins = 500. Step 4: Experimental probability = 235 / 500 = 0.47. Step 5: Round to nearest hundredth: 0.47 is already at the hundredths place. The answer is 0.47.

  3. Tane rolled a standard six-sided die 135 times. He recorded the number 3 appearing 27 times. Approximate P(3). Answer: 0.2 Solution: Identify the number of times the event occurred: 27 times. Identify the total number of trials: 135 rolls. Calculate the relative frequency: 27 ÷ 135 = 0.2.
    Full step-by-step solution

    Step 1: Identify the number of times the event occurred: 27 times. Step 2: Identify the total number of trials: 135 rolls. Step 3: Calculate the relative frequency: 27 ÷ 135 = 0.2. Step 4: The approximate probability P(3) is 0.2. The answer is 0.2.

  4. Noah is testing a new board game that uses a spinner divided into 4 equal sections labeled A, B, C, and D. He spins the spinner 500 times and records the results. The table below shows how many times each letter appeared: A: 132 times B: 118 times C: 127 times D: 123 times Based on Noah's experimental data, what is the approximate probability that the spinner will land on a letter that comes before C in the alphabet? Express your answer as a decimal rounded to the nearest hundredth. Answer: 0.50 Solution: Identify the letters that come before C in the alphabet: A and B. Add their frequencies: A appeared 132 times, B appeared 118 times. Total = 132 + 118 = 250 times.
    Full step-by-step solution

    Step 1: Identify the letters that come before C in the alphabet: A and B. Step 2: Add their frequencies: A appeared 132 times, B appeared 118 times. Total = 132 + 118 = 250 times. Step 3: Total number of spins = 500. Step 4: Experimental probability = 250 / 500 = 0.5. Step 5: Round to nearest hundredth: 0.5 rounds to 0.50. The answer is 0.50.

  5. Mere is conducting a probability experiment by flipping a fair coin. She flips the coin 8,000 times and records that it lands on heads 4,128 times. Based on her experimental data, what is the approximate experimental probability of flipping heads? Express your answer as a decimal rounded to the nearest thousandth. Answer: 0.516 Solution: Identify the number of successful outcomes. The event is flipping heads, which occurred 4,128 times. Identify the total number of trials.
    Full step-by-step solution

    Step 1: Identify the number of successful outcomes. The event is flipping heads, which occurred 4,128 times. Step 2: Identify the total number of trials. Mere flipped the coin 8,000 times. Step 3: Calculate the experimental probability: successful outcomes / total trials = 4,128 / 8,000. Step 4: Perform the division: 4,128 ÷ 8,000 = 0.516. Step 5: Round to the nearest thousandth. The decimal is already 0.516, so no rounding is needed. Therefore, the experimental probability of flipping heads is 0.516.

  6. Emma rolled a standard six-sided die 80 times. She recorded the number 5 appearing 15 times. Approximate P(5). Answer: 0.1875 Solution: Identify the number of times the event occurred: 15 times. Identify the total number of trials: 80 rolls. Calculate the relative frequency: 15 ÷ 80 = 0.1875.
    Full step-by-step solution

    Step 1: Identify the number of times the event occurred: 15 times. Step 2: Identify the total number of trials: 80 rolls. Step 3: Calculate the relative frequency: 15 ÷ 80 = 0.1875. Step 4: The approximate probability P(5) is 0.1875. The answer is 0.1875.

  7. A school is conducting a survey about favorite school subjects. In a random sample of 200 students, 45 students chose mathematics as their favorite subject. Based on this sample, approximately how many students would you expect to choose mathematics as their favorite subject if the entire school has 1,240 students? Answer: 279 Solution: We have a sample of 200 students, and 45 of them chose mathematics as their favorite subject.
    Full step-by-step solution

    Step 1: Understand the problem We have a sample of 200 students, and 45 of them chose mathematics as their favorite subject. We want to estimate how many students in the whole school (1,240 students) would choose mathematics, assuming the same proportion holds. Step 2: Find the proportion in the sample The proportion of students who like mathematics in the sample is: 45 / 200 Step 3: Simplify the fraction 45/200 = 9/40 (by dividing numerator and denominator by 5) We can also compute the decimal: 45 ÷ 200 = 0.225 Step 4: Apply the proportion to the whole school Multiply the proportion by the total number of students in the school: (45 / 200) × 1240 Step 5: Perform the calculation First, 45 × 1240 = 45 × 1000 + 45 × 240 = 45000 + 10800 = 55800 Now divide by 200: 55800 ÷ 200 = 279 Step 6: Interpret the result We expect approximately 279 students in the entire school to choose mathematics as their favorite subject. Final answer: 279