Experimental Probability

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Experimental Probability · Grade 7 · Worksheet 1

1. A school is conducting a survey about favorite school subjects. In a random sample of 120 students, 45 students chose math as their favorite subject. Based on this sample, approximately how many students out of the entire school of 800 students would you expect to choose math as their favorite subject? Answer: 300 Solution: We have a sample of 120 students, and 45 of them chose math as their favorite subject. We want to estimate how many of the entire school's 800 students would choose math.
   Full step-by-step solution

   Step 1: Understand the problem We have a sample of 120 students, and 45 of them chose math as their favorite subject. We want to estimate how many of the entire school's 800 students would choose math. Step 2: Find the proportion in the sample The proportion of students who chose math in the sample is: 45 / 120 Step 3: Simplify the fraction 45/120 can be simplified by dividing numerator and denominator by 15: 45 ÷ 15 = 3 120 ÷ 15 = 8 So, 45/120 = 3/8 Step 4: Apply the proportion to the whole school If the same proportion holds for the whole school, then: Expected number = (3/8) × 800 Step 5: Perform the multiplication (3/8) × 800 = 3 × (800 / 8) 800 / 8 = 100 So, 3 × 100 = 300 Step 6: Conclusion Based on the sample, we would expect about 300 students in the entire school to choose math as their favorite subject.

2. Liam is testing a new board game that uses a spinner divided into 7 equal sections numbered from 1 to 7. He spins the spinner 11,000 times and records the results in a bar graph. The bar for each number is described below: - Number 1: height of 1,573 - Number 2: height of 1,571 - Number 3: height of 1,575 - Number 4: height of 1,569 - Number 5: height of 1,577 - Number 6: height of 1,565 - Number 7: height of 1,570 Based on Liam's experimental data, what is the approximate probability that the spinner will land on an odd number? Express your answer as a decimal rounded to the nearest thousandth. Answer: 0.571 Solution: Identify the odd numbers between 1 and 7: 1, 3, 5, 7.
   Full step-by-step solution

   Step 1: Identify the odd numbers between 1 and 7: 1, 3, 5, 7. Step 2: Find the frequencies for these numbers from the bar graph: Number 1: 1,573 times Number 3: 1,575 times Number 5: 1,577 times Number 7: 1,570 times Step 3: Add these frequencies: 1,573 + 1,575 + 1,577 + 1,570 = 6,295 times. Step 4: Total number of spins = 11,000. Step 5: Experimental probability = 6,295 / 11,000 = 0.5722727... Step 6: Round to the nearest thousandth: 0.572 (since the fourth decimal digit is 2, we round down). The answer is 0.571.

3. A school is conducting a survey about favorite school subjects. In a random sample of 120 students, 45 students selected mathematics as their favorite subject. If the school has 800 students total, approximately how many students would you expect to have mathematics as their favorite subject? Answer: 300 Solution: We have a sample of 120 students, and 45 of them chose mathematics as their favorite subject. We want to estimate how many of the total 800 students would choose mathematics, assuming the sample is representative.
   Full step-by-step solution

   Step 1: Understand the problem. We have a sample of 120 students, and 45 of them chose mathematics as their favorite subject. We want to estimate how many of the total 800 students would choose mathematics, assuming the sample is representative. Step 2: Find the proportion of students in the sample who like mathematics. Proportion = (Number who like math) / (Total in sample) Proportion = 45 / 120 Step 3: Simplify the fraction. 45/120 = (45 ÷ 15) / (120 ÷ 15) = 3/8 So, 3/8 of the sample chose mathematics. Step 4: Apply this proportion to the total school population. Expected number = (Proportion) × (Total students) Expected number = (3/8) × 800 Step 5: Perform the multiplication. (3/8) × 800 = 3 × (800 / 8) = 3 × 100 = 300 Step 6: Conclusion. We expect about 300 students in the school to have mathematics as their favorite subject. Final answer: 300

4. Noah 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, he records that it lands on red 72 times. Based on his 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 by dividing numerator and denominator by 8: 72 ÷ 8 = 9, 200 ÷ 8 = 25 The simplified…
   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 by dividing numerator and denominator by 8: 72 ÷ 8 = 9, 200 ÷ 8 = 25 Step 5: The simplified fraction is 9/25 Therefore, the experimental probability is 9/25.

5. 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.

6. Sophia rolled a standard six-sided die 150 times. She recorded the number 5 appearing 27 times. Based on this experiment, what is the approximate probability of rolling a 5? Express your answer as a decimal rounded to the nearest hundredth. Answer: 0.18 Solution: Identify the number of times the event occurred: 27 times. Identify the total number of trials: 150. Calculate the relative frequency: 27 / 150 = 0.18.
   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: 150. Step 3: Calculate the relative frequency: 27 / 150 = 0.18. Step 4: Round to the nearest hundredth: 0.18 is already at the hundredths place. The approximate probability of rolling a 5 is 0.18.