# Experimental Probability Worksheet ## Section A: Multiple Choice Questions
Q1: A coin is flipped 50 times and lands on heads 28 times. What is the experimental probability of getting heads? (a) \(\frac{28}{50}\) (b) \(\frac{1}{2}\) (c) \(\frac{22}{50}\) (d) \(\frac{28}{100}\)
Solution:
Ans: (a) Explanation:Experimental probability is calculated as the ratio of the number of times an event occurs to the total number of trials. Here, heads occurred 28 times out of 50 flips, so the experimental probability is \(\frac{28}{50}\) or 0.56. Option (b) represents theoretical probability, not experimental. Option (c) represents tails, and option (d) incorrectly doubles the denominator.
Q2: A student rolls a die 60 times and records the number of times each number appears. This type of probability is called: (a) Theoretical probability (b) Experimental probability (c) Subjective probability (d) Classical probability
Solution:
Ans: (b) Explanation:Experimental probability is based on actual trials and observations. The student is conducting an experiment by rolling the die 60 times and recording results. Theoretical probability is based on what should happen mathematically, not what actually happens in trials.
Q3: A basketball player makes 15 free throws out of 25 attempts. Based on this data, what is the experimental probability that she will miss her next free throw? (a) \(\frac{15}{25}\) (b) \(\frac{10}{25}\) (c) \(\frac{15}{10}\) (d) \(\frac{25}{15}\)
Solution:
Ans: (b) Explanation: If the player made 15 out of 25 free throws, then she missed \(25 - 15 = 10\) free throws. The experimental probability of missing is \(\frac{10}{25}\) or \(\frac{2}{5}\). Option (a) represents making the shot, while options (c) and (d) have numerator and denominator reversed or incorrect.
Q4: A spinner is spun 80 times. The results show: Red = 32, Blue = 28, Green = 20. What is the experimental probability of landing on Blue? (a) \(\frac{32}{80}\) (b) \(\frac{28}{80}\) (c) \(\frac{20}{80}\) (d) \(\frac{28}{60}\)
Solution:
Ans: (b) Explanation: The experimental probability is the number of times Blue appeared divided by the total number of spins. Blue appeared 28 times out of 80 total spins, giving \(\frac{28}{80}\) or \(\frac{7}{20}\). Option (a) represents Red, option (c) represents Green, and option (d) uses an incorrect denominator.
Q5: As the number of trials in an experiment increases, the experimental probability tends to: (a) Become less accurate (b) Approach the theoretical probability (c) Always equal 1 (d) Decrease to zero
Solution:
Ans: (b) Explanation: This describes the Law of Large Numbers, which states that as the number of trials increases, the experimental probability gets closer to the theoretical probability. More trials generally lead to more accurate results, not less accurate. Experimental probability does not necessarily equal 1 or approach zero.
Q6: A bag contains colored marbles. In 100 random draws (with replacement), red was drawn 45 times, blue 35 times, and yellow 20 times. What is the experimental probability of NOT drawing red? (a) \(\frac{45}{100}\) (b) \(\frac{55}{100}\) (c) \(\frac{35}{100}\) (d) \(\frac{80}{100}\)
Solution:
Ans: (b) Explanation: The probability of NOT drawing red is found by subtracting the number of red draws from the total: \(100 - 45 = 55\). Thus, the experimental probability is \(\frac{55}{100}\) or 0.55. Option (a) represents drawing red, option (c) only represents blue, and option (d) incorrectly adds blue and yellow then uses wrong calculation.
Q7: A quality control inspector finds 8 defective items in a sample of 200 products. What is the experimental probability that a randomly selected item from this production batch is NOT defective? (a) \(\frac{8}{200}\) (b) \(\frac{192}{200}\) (c) \(\frac{200}{192}\) (d) \(\frac{8}{192}\)
Solution:
Ans: (b) Explanation: If 8 items are defective out of 200, then \(200 - 8 = 192\) items are NOT defective. The experimental probability of selecting a non-defective item is \(\frac{192}{200}\) or 0.96. Option (a) represents defective items, while options (c) and (d) have incorrect ratios.
Q8: Which statement about experimental probability is TRUE? (a) It is always equal to theoretical probability (b) It cannot be expressed as a decimal (c) It is based on actual results from experiments (d) It requires no trials to calculate
Solution:
Ans: (c) Explanation:Experimental probability is based on actual observed results from conducting trials or experiments. It may differ from theoretical probability (option a is false), can be expressed as a fraction, decimal, or percentage (option b is false), and requires trials to calculate (option d is false).
## Section B: Fill in the Blanks Q9: Experimental probability is calculated by dividing the number of times an event occurs by the total number of __________.
Solution:
Ans: trials Explanation: The formula for experimental probability is: \(\text{Experimental Probability} = \frac{\text{Number of times event occurs}}{\text{Total number of trials}}\). The denominator represents all the trials or experiments conducted.
Q10: The __________ states that as the number of trials increases, experimental probability gets closer to theoretical probability.
Solution:
Ans: Law of Large Numbers Explanation: The Law of Large Numbers is a fundamental principle in probability that describes how experimental results become more predictable and approach theoretical values as the sample size increases.
Q11: If a die is rolled 120 times and the number 5 appears 18 times, the experimental probability of rolling a 5 is __________ when expressed as a decimal.
Solution:
Ans: 0.15 Explanation: The experimental probability is \(\frac{18}{120} = 0.15\). This represents 15% or a 15 in 100 chance based on the experimental data collected.
Q12: Probability expressed as a ratio of favorable outcomes from actual experiments is called __________ probability.
Solution:
Ans: experimental Explanation:Experimental probability is determined by conducting actual trials and recording outcomes, as opposed to theoretical probability which is based on mathematical calculations of what should happen.
Q13: If an event never occurs in 50 trials, the experimental probability of that event is __________.
Solution:
Ans: 0 Explanation: If an event occurs 0 times in 50 trials, the experimental probability is \(\frac{0}{50} = 0\). This means the event did not happen in any of the trials conducted, though it doesn't mean it's impossible.
Q14: Experimental probability can be written as a fraction, decimal, or __________.
Solution:
Ans: percentage Explanation:Probability can be expressed in three equivalent forms: as a fraction (like \(\frac{1}{4}\)), as a decimal (like 0.25), or as a percentage (like 25%). All three represent the same likelihood.
## Section C: Word Problems Q15: A traffic engineer records the color of 150 cars passing through an intersection. She observes 60 white cars, 45 black cars, 30 silver cars, and 15 red cars. Based on this data, what is the experimental probability that the next car passing through will be either white or black? Express your answer as a simplified fraction.
Solution:
Ans: Number of white or black cars = \(60 + 45 = 105\) Total number of cars = 150 Experimental probability = \(\frac{105}{150} = \frac{7}{10}\) Final Answer: \(\frac{7}{10}\) or 0.7
Q16: A meteorologist records weather data for 365 days in a year. It rained on 73 days, was sunny on 219 days, and was cloudy (no rain) on 73 days. What is the experimental probability that a randomly selected day from this year was sunny? Express your answer as a decimal rounded to the nearest hundredth.
Solution:
Ans: Number of sunny days = 219 Total number of days = 365 Experimental probability = \(\frac{219}{365}\) \(\frac{219}{365} = 0.6\) Final Answer: 0.60
Q17: A pharmaceutical company tests a new medication on 500 patients. The medication is effective for 380 patients. Based on this experimental data, if 1,250 patients take this medication, approximately how many patients would you expect the medication to be effective for?
Solution:
Ans: Experimental probability of effectiveness = \(\frac{380}{500} = 0.76\) Expected number of patients = \(1,250 \times 0.76\) \(1,250 \times 0.76 = 950\) Final Answer: 950 patients
Q18: A baseball player's batting statistics show 156 hits in 520 at-bats during a season. Calculate the experimental probability of the player getting a hit in an at-bat. Express your answer as a simplified fraction and as a decimal rounded to three decimal places.
Solution:
Ans: Experimental probability = \(\frac{156}{520}\) Simplifying: \(\frac{156}{520} = \frac{39}{130}\) As a decimal: \(\frac{39}{130} = 0.3\) Final Answer: \(\frac{39}{130}\) or 0.300
Q19: A spinner is divided into 4 equal sections colored red, blue, green, and yellow. Maya spins it 200 times and records: Red = 58, Blue = 52, Green = 48, Yellow = 42. Compare the experimental probability of landing on red with the theoretical probability. What is the difference between these two probabilities? Express your answer as a decimal.
Solution:
Ans: Experimental probability of red = \(\frac{58}{200} = 0.29\) Theoretical probability of red = \(\frac{1}{4} = 0.25\) Difference = \(0.29 - 0.25 = 0.04\) Final Answer: 0.04
Q20: A factory produces light bulbs, and quality control tests 800 bulbs. They find that 752 bulbs work properly and 48 are defective. What is the experimental probability that a bulb is defective? If the factory produces 25,000 bulbs in a month, approximately how many would you expect to be defective based on this experimental data?
Solution:
Ans: Experimental probability of defective bulb = \(\frac{48}{800} = \frac{3}{50} = 0.06\) Expected defective bulbs in 25,000 = \(25,000 \times 0.06\) \(25,000 \times 0.06 = 1,500\) Final Answer: The experimental probability is 0.06, and approximately 1,500 bulbs would be expected to be defective.
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