Experimental Probability

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Experimental Probability · Grade 7 · Worksheet 2

1. A school is conducting a survey about favorite after-school activities. In a random sample of 120 students, 45 students chose sports, 30 chose music, 25 chose art, and 20 chose reading. If the school has 800 students total, based on this sample, approximately how many students would you expect to choose sports as their favorite activity? Answer: 300 Solution: We have a sample of 120 students, and 45 of them chose sports. We want to estimate how many of the total 800 students would choose sports, 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 sports. We want to estimate how many of the total 800 students would choose sports, assuming the sample is representative. Step 2: Find the proportion of students in the sample who chose sports. Proportion = (Number who chose sports) / (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 sports. 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. Based on the sample, we would expect about 300 students in the school to choose sports as their favorite activity. Final answer: 300

2. 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

3. Emma is conducting a probability experiment with a spinner divided into 8 equal sections labeled 1 through 8. She spins the spinner 200 times and records that it lands on an even number 112 times. Based on her experiment, what is the experimental probability of the spinner landing on an even number? Express your answer as a simplified fraction. Answer: 14/25 Solution: Identify the number of successful outcomes (even numbers): 112 Identify the total number of trials: 200 Calculate experimental probability: 112/200 Simplify the fraction by dividing numerator and denominator by 8: 112 ÷ 8 = 14, 200 ÷ 8 = 25 The simplified fraction is 14/25 Therefore, the…
   Full step-by-step solution

   Step 1: Identify the number of successful outcomes (even numbers): 112 Step 2: Identify the total number of trials: 200 Step 3: Calculate experimental probability: 112/200 Step 4: Simplify the fraction by dividing numerator and denominator by 8: 112 ÷ 8 = 14, 200 ÷ 8 = 25 Step 5: The simplified fraction is 14/25 Therefore, the experimental probability is 14/25.

4. 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.

5. Maya 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 blue 47 times. Based on her experiment, what is the experimental probability of the spinner landing on blue? Express your answer as a simplified fraction. Answer: 47/200 Solution: Identify the number of successful outcomes (blue spins) = 47 Identify the total number of trials = 200 Calculate experimental probability = successful outcomes / total trials Experimental probability = 47/200 Check if the fraction can be simplified: 47 is a prime number, and 200 is not divisible…
   Full step-by-step solution

   Step 1: Identify the number of successful outcomes (blue spins) = 47 Step 2: Identify the total number of trials = 200 Step 3: Calculate experimental probability = successful outcomes / total trials Step 4: Experimental probability = 47/200 Step 5: Check if the fraction can be simplified: 47 is a prime number, and 200 is not divisible by 47, so 47/200 is already simplified The answer is 47/200.

6. A school is conducting a survey about favorite school subjects. They randomly select 120 students from the 7th grade. The results show that 45 students prefer math, 30 prefer science, 25 prefer English, and 20 prefer history. If the school has 480 students in total across all grades, and they want to predict how many students in the entire school prefer math based on this sample, how many students would that be? Answer: 180 Solution: We have a sample of 120 students from the 7th grade. In this sample, 45 students prefer math. We want to predict how many of the total 480 students in the school prefer math, assuming the sample is representative.
   Full step-by-step solution

   Step 1: Understand the problem We have a sample of 120 students from the 7th grade. In this sample, 45 students prefer math. We want to predict how many of the total 480 students in the school prefer math, assuming the sample is representative. Step 2: Find the fraction of students who prefer math in the sample Number of students in sample who prefer math = 45 Total number of students in sample = 120 Fraction = 45 / 120 Step 3: Simplify the fraction 45 / 120 = (45 ÷ 15) / (120 ÷ 15) = 3 / 8 So, 3/8 of the sample students prefer math. Step 4: Apply the fraction to the whole school Total students in school = 480 Predicted number who prefer math = (3/8) × 480 Step 5: Calculate First, 480 ÷ 8 = 60 Then, 60 × 3 = 180 Step 6: Conclusion Based on the sample, we predict that 180 students in the entire school prefer math. Final answer: 180