Math Problem Statement
Solution
To analyze this problem, let’s first break down the details provided:
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Pen Composition: The box has 1 red pen, 2 black pens, and 3 blue pens. This makes a total of pens.
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Theoretical Probability of Blue Pen: The probability of pulling a blue pen from the box is calculated as:
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Experimental Observation: Ron pulls a pen out 4 times and only gets a blue pen once. This observed frequency suggests that in his experiment, the chance of pulling a blue pen seems lower than the theoretical probability.
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Law of Large Numbers: Ron believes that as he increases the number of trials (pulling pens), the observed frequency (experimental probability) of pulling a blue pen will get closer to the theoretical probability.
Given the answer choices:
- The correct answer should reflect that the experimental probability will get closer to the theoretical probability (1/2) as the number of trials increases. This is based on the principle of the Law of Large Numbers, which states that the more trials conducted, the closer the experimental probability will align with the theoretical probability.
Therefore, the correct answer is: "The experimental probability of pulling a blue pen based on the observed frequency will get closer to as the number of trials increases."
Would you like further explanation on probability concepts, or do you have additional questions?
Here are five related questions that might help you explore this topic further:
- What is the difference between theoretical and experimental probability?
- How does the Law of Large Numbers influence probability experiments?
- Why might experimental probability differ from theoretical probability in a small sample size?
- How would increasing the number of trials affect the accuracy of experimental probability?
- Can the experimental probability ever be exactly equal to the theoretical probability?
Tip: Remember that experimental probability often fluctuates with a smaller number of trials, but it generally stabilizes closer to the theoretical probability as trials increase.
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Math Problem Analysis
Mathematical Concepts
Probability
Experimental Probability
Theoretical Probability
Law of Large Numbers
Formulas
Theoretical Probability = (Number of favorable outcomes) / (Total number of outcomes)
Theorems
Law of Large Numbers
Suitable Grade Level
Grade 7-9
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