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Experimental Probability

Grade 7 · Statistics · Worksheet 3

  1. Emma is conducting a probability experiment with a spinner divided into 8 equal sections: 3 red, 2 blue, 2 green, and 1 yellow. After spinning it 200 times, she records that it lands on red 72 times. Based on her experiment, what is the experimental probability of the spinner landing on red? Express your answer as a simplified fraction. Answer: ______________
  2. (-4)² - 3 × (18 ÷ 6 + 2) = ? Answer: ______________
  3. Noah is conducting a science experiment where he drops a marble onto a grid of 10 equal-sized squares numbered 1 through 10. He drops the marble 500 times and records which square it lands in. The results are shown in the bar graph below (described in text): - Square 1: 48 times - Square 2: 52 times - Square 3: 47 times - Square 4: 53 times - Square 5: 49 times - Square 6: 51 times - Square 7: 50 times - Square 8: 52 times - Square 9: 48 times - Square 10: 50 times Based on Noah's experimental data, what is the approximate probability that the marble lands on a square with a number that is a multiple of 3? Express your answer as a decimal rounded to the nearest hundredth. Answer: ______________
  4. Liam is conducting a probability experiment with a standard six-sided die. He wants to determine the experimental probability of rolling a number greater than 4. After rolling the die 120 times, he recorded 38 outcomes where the result was greater than 4. Based on his experiment, what is the approximate experimental probability of rolling a number greater than 4? Express your answer as a decimal rounded to the nearest hundredth. Answer: ______________
  5. A factory produces 15,000 electronic components per day. Quality control testing shows that approximately 3.2% of components are defective. If the factory operates for 5 days, approximately how many defective components would you expect them to produce in total? Answer: ______________
  6. Aroha is conducting a probability experiment with a standard six-sided die. She rolls the die 12,000 times and records that she rolled a number less than 3 exactly 3,850 times. Based on her experimental data, what is the experimental probability of rolling a number less than 3? 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. Emma is conducting a probability experiment with a spinner divided into 8 equal sections: 3 red, 2 blue, 2 green, and 1 yellow. After spinning it 200 times, she records that it lands on red 72 times. Based on her experiment, what is the experimental probability of the spinner landing on red? Express your answer as a simplified fraction. Answer: 9/25 Solution: Identify the number of successful outcomes (red spins): 72 Identify the total number of trials: 200 Calculate experimental probability: successful outcomes / total trials = 72/200 Simplify the fraction: divide numerator and denominator by 8, which gives 9/25 The simplified fraction is 9/25…
    Full step-by-step solution

    Step 1: Identify the number of successful outcomes (red spins): 72 Step 2: Identify the total number of trials: 200 Step 3: Calculate experimental probability: successful outcomes / total trials = 72/200 Step 4: Simplify the fraction: divide numerator and denominator by 8, which gives 9/25 Step 5: The simplified fraction is 9/25 Therefore, the experimental probability is 9/25.

  2. (-4)² - 3 × (18 ÷ 6 + 2) = ? Answer: 1 Solution: Solve inside the parentheses: 18 ÷ 6 + 2 = 3 + 2 = 5 Calculate the exponent: (-4)² = 16 Perform the multiplication: 3 × 5 = 15 Complete the subtraction: 16 - 15 = 1 The final answer is 1.
    Full step-by-step solution

    Step 1: Solve inside the parentheses: 18 ÷ 6 + 2 = 3 + 2 = 5 Step 2: Calculate the exponent: (-4)² = 16 Step 3: Perform the multiplication: 3 × 5 = 15 Step 4: Complete the subtraction: 16 - 15 = 1 Step 5: The final answer is 1.

  3. Noah is conducting a science experiment where he drops a marble onto a grid of 10 equal-sized squares numbered 1 through 10. He drops the marble 500 times and records which square it lands in. The results are shown in the bar graph below (described in text): - Square 1: 48 times - Square 2: 52 times - Square 3: 47 times - Square 4: 53 times - Square 5: 49 times - Square 6: 51 times - Square 7: 50 times - Square 8: 52 times - Square 9: 48 times - Square 10: 50 times Based on Noah's experimental data, what is the approximate probability that the marble lands on a square with a number that is a multiple of 3? Express your answer as a decimal rounded to the nearest hundredth. Answer: 0.29 Solution: Identify the multiples of 3 between 1 and 10: 3, 6, 9. Find the frequencies for those squares from the data: Square 3: 47 times Square 6: 51 times Square 9: 48 times Add the frequencies: 47 + 51 + 48 = 146 times.
    Full step-by-step solution

    Step 1: Identify the multiples of 3 between 1 and 10: 3, 6, 9. Step 2: Find the frequencies for those squares from the data: Square 3: 47 times Square 6: 51 times Square 9: 48 times Step 3: Add the frequencies: 47 + 51 + 48 = 146 times. Step 4: Total number of drops = 500. Step 5: Experimental probability = 146 / 500 = 0.292. Step 6: Round 0.292 to the nearest hundredth: The thousandths digit is 2, which is less than 5, so we round down to 0.29. The answer is 0.29.

  4. Liam is conducting a probability experiment with a standard six-sided die. He wants to determine the experimental probability of rolling a number greater than 4. After rolling the die 120 times, he recorded 38 outcomes where the result was greater than 4. Based on his experiment, what is the approximate experimental probability of rolling a number greater than 4? Express your answer as a decimal rounded to the nearest hundredth. Answer: 0.32 Solution: Liam rolled a die 120 times and got a number greater than 4 on 38 rolls. On a standard six-sided die, numbers greater than 4 are 5 and 6.
    Full step-by-step solution

    Step 1: Understand the problem. Liam rolled a die 120 times and got a number greater than 4 on 38 rolls. On a standard six-sided die, numbers greater than 4 are 5 and 6. Experimental probability = (number of successful outcomes) / (total number of trials). Step 2: Identify the numbers from the experiment. Successful outcomes = 38 Total trials = 120 Step 3: Write the experimental probability as a fraction. Probability = 38 / 120 Step 4: Simplify the fraction if possible. Both 38 and 120 are divisible by 2: 38 ÷ 2 = 19 120 ÷ 2 = 60 So, 38/120 = 19/60 Step 5: Convert the fraction to a decimal. Divide 19 by 60: 19 ÷ 60 = 0.31666... Step 6: Round to the nearest hundredth. 0.31666... → Look at the thousandths digit: it is 6, which is 5 or greater, so round the hundredths digit (1) up to 2. Thus, 0.31666... ≈ 0.32 Step 7: Final answer. The experimental probability is approximately 0.32.

  5. A factory produces 15,000 electronic components per day. Quality control testing shows that approximately 3.2% of components are defective. If the factory operates for 5 days, approximately how many defective components would you expect them to produce in total? Answer: 2400 Solution: Find the number of defective components produced in one day. The factory makes 15,000 components per day, and 3.2% are defective. 3.2% as a decimal is 3.2 / 100 = 0.032.
    Full step-by-step solution

    Step 1: Find the number of defective components produced in one day. The factory makes 15,000 components per day, and 3.2% are defective. 3.2% as a decimal is 3.2 / 100 = 0.032. Defectives per day = 15,000 × 0.032. Step 2: Calculate 15,000 × 0.032. First, 15,000 × 0.03 = 450. Then, 15,000 × 0.002 = 30. Add them: 450 + 30 = 480 defective components per day. Step 3: Multiply by the number of days the factory operates. Days = 5. Total defective components = 480 × 5 = 2,400. Step 4: Conclusion. Over 5 days, the factory is expected to produce about 2,400 defective components. Final answer: 2400

  6. Aroha is conducting a probability experiment with a standard six-sided die. She rolls the die 12,000 times and records that she rolled a number less than 3 exactly 3,850 times. Based on her experimental data, what is the experimental probability of rolling a number less than 3? Express your answer as a decimal rounded to the nearest thousandth. Answer: 0.321 Solution: Identify the number of successful outcomes. The event is rolling a number less than 3, which means rolling a 1 or a 2. Aroha recorded this event 3,850 times.
    Full step-by-step solution

    Step 1: Identify the number of successful outcomes. The event is rolling a number less than 3, which means rolling a 1 or a 2. Aroha recorded this event 3,850 times. Step 2: Identify the total number of trials. Aroha rolled the die 12,000 times. Step 3: Calculate the experimental probability: successful outcomes / total trials = 3,850 / 12,000. Step 4: Convert the fraction to a decimal: 3,850 divided by 12,000 = 0.3208333... Step 5: Round to the nearest thousandth. The ten-thousandths digit is 8, which is 5 or greater, so we round up the thousandths digit. 0.320833... rounded to the nearest thousandth is 0.321. Therefore, the experimental probability of rolling a number less than 3 is 0.321.