Experimental Probability

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Experimental Probability · Grade 7 · Worksheet 2

1. Emma is conducting a probability experiment with a spinner divided into 8 equal sections: 3 red, 2 blue, 2 green, and 1 yellow. She spins the spinner 200 times and records the results. If the experimental probability of landing on red is 0.38, how many times did the spinner land on red during her experiment? Answer: 76 Solution: Recall that experimental probability = (number of successful outcomes) / (total number of trials) In this problem, the experimental probability for red is given as 0.38 and the total number of trials is 200 Set up the equation: 0.38 = (number of red outcomes) / 200 Multiply both sides by 200:…
   Full step-by-step solution

   Step 1: Recall that experimental probability = (number of successful outcomes) / (total number of trials) Step 2: In this problem, the experimental probability for red is given as 0.38 and the total number of trials is 200 Step 3: Set up the equation: 0.38 = (number of red outcomes) / 200 Step 4: Multiply both sides by 200: 0.38 × 200 = number of red outcomes Step 5: Calculate: 0.38 × 200 = 76 Step 6: Therefore, the spinner landed on red 76 times during the experiment.

2. 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.

3. (-3)² + 4 × (-5) = ? Answer: -11 Solution: Evaluate (-3)² (-3) × (-3) = 9 So, (-3)² = 9. Evaluate 4 × (-5) 4 × (-5) = -20. 9 + (-20) = 9 - 20 = -11.
   Full step-by-step solution

   Let's solve step by step. Step 1: Evaluate (-3)² A negative number squared becomes positive: (-3) × (-3) = 9 So, (-3)² = 9. Step 2: Evaluate 4 × (-5) A positive times a negative gives a negative: 4 × (-5) = -20. Step 3: Add the results 9 + (-20) = 9 - 20 = -11. Final answer: -11

4. 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.

5. 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. If the school has 1,250 students total, approximately how many students would you expect to choose mathematics as their favorite subject? Answer: 281 Solution: We have a sample of 200 students, and 45 of them chose mathematics as their favorite subject. We want to estimate how many of the total 1,250 students would choose mathematics, assuming the sample is representative.
   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 of the total 1,250 students would choose mathematics, assuming the sample is representative. Step 2: Find the proportion from the sample The proportion of students who like mathematics in the sample is: 45 / 200 Step 3: Simplify the fraction 45 / 200 = 9 / 40 (We divide numerator and denominator by 5.) Step 4: Apply the proportion to the total population If the same proportion holds for the whole school, the expected number of students who choose mathematics is: (9 / 40) × 1250 Step 5: Perform the multiplication First, 1250 / 40 = 31.25 Then, 31.25 × 9 = 281.25 Step 6: Round appropriately Since we can’t have a fraction of a person, we round to the nearest whole number. 281.25 rounds to 281. Final answer: 281

6. A school is conducting a survey about favorite after-school activities. They randomly select 120 students from the 7th grade. The results show that 45 students prefer sports, 30 prefer arts and crafts, 25 prefer reading, and 20 prefer music. Based on this sample, if there are 480 students in the entire 7th grade, approximately how many students would you expect to prefer sports? Answer: 180 Solution: We have a sample of 120 students from the 7th grade. In this sample, 45 students prefer sports.
   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 sports. We want to estimate how many of the total 480 students in the 7th grade prefer sports, assuming the sample is representative. Step 2: Find the proportion of students who prefer sports in the sample Proportion = (Number who prefer sports in sample) / (Total in sample) Proportion = 45 / 120 Step 3: Simplify the proportion 45/120 = (45 ÷ 15) / (120 ÷ 15) = 3/8 So, 3/8 of the sample prefers sports. Step 4: Apply the proportion to the entire grade If 3/8 of the sample prefers sports, we expect about 3/8 of the whole grade to prefer sports. Number expected = (3/8) × (Total students in grade) Number expected = (3/8) × 480 Step 5: Calculate (3/8) × 480 = 3 × (480 / 8) 480 / 8 = 60 3 × 60 = 180 Step 6: Conclusion We would expect about 180 students in the entire 7th grade to prefer sports.

7. Aroha spun a spinner with 7 equal sections 135 times. The spinner landed on red 27 times. Approximate P(red). Answer: 0.2 Solution: Identify the number of times the event occurred: 27 (landed on red). Identify the total number of trials: 135 spins. Divide the event count by the total trials: 27 ÷ 135 = 27/135.
   Full step-by-step solution

   Step 1: Identify the number of times the event occurred: 27 (landed on red). Step 2: Identify the total number of trials: 135 spins. Step 3: Divide the event count by the total trials: 27 ÷ 135 = 27/135. Step 4: Simplify the fraction: 27/135 = 1/5 (since 27 × 5 = 135). Step 5: Convert to decimal: 1/5 = 0.2. The approximate probability of landing on red is 0.2.

8. Isabella rolled a standard six-sided die 250 times. She recorded the number 2 appearing 42 times. Approximate P(2). Answer: 0.168 Solution: Identify the number of times the event occurred: 42 times. Identify the total number of trials: 250 rolls. Calculate the relative frequency: 42 ÷ 250 = 0.168.
   Full step-by-step solution

   Step 1: Identify the number of times the event occurred: 42 times. Step 2: Identify the total number of trials: 250 rolls. Step 3: Calculate the relative frequency: 42 ÷ 250 = 0.168. Step 4: The approximate probability P(2) is 0.168. The answer is 0.168.