Questions and Answers
What is empirical probability?
uses actual data to determine the numerical probability that an event will happen
What is subjective probability?
A probability value based on an educated guess or estimate, employing opinions and inexact information
What is the formula for empirical probability?
P(E) = frequency of event E / Total Frequency
Finding the probability of rolling a dice three times and getting 6 three times in a row is an example of which type of probability?
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What is the law of large numbers?
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A phone manufacturer finds that 1 out of every 378 phones is defective. Is this an example of classical, empirical, or subjective probability?
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If a coin is flipped 8 times and all 8 times it lands on heads, thinking the next flip has a 100% chance of being tails is an example of which type of probability?
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Classical probability uses the sample space, while empirical probability uses ______.
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What is the probability that the next person Julia interviews is satisfied if 17 out of 35 said they were satisfied?
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If Georgina's survey indicates 9 students own cars, 17 use parents' cars, and 35 have no cars, what is the probability the next student has no car?
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Jill flips a coin 6 times and gets 4 heads and 2 tails. What is the probability she gets heads on her next flip?
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What is the actual probability Kiara will flip heads on her next flip after flipping 4 heads and 2 tails in 6 attempts?
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Study Notes
Empirical Probability
- Defined as the probability determined using actual data rather than theoretical predictions.
- Formula: P(E) = frequency of event E / Total Frequency.
- Example: A study shows that 1 in 378 phone units is defective, demonstrating empirical probability.
Subjective Probability
- Represents a probability value derived from personal judgment or estimation rather than exact data.
- Example: Believing that after flipping 8 heads consecutively, the next flip will definitely be tails reflects subjective probability.
Classical Probability
- Based on theoretical models and the assumption of equally likely outcomes.
- Example: The probability of rolling a 6 three times in a row on a fair die is calculated theoretically.
Law of Large Numbers
- Describes how as experiments are repeated, empirical probabilities converge towards classical probabilities, emphasizing the relationship between the two.
Key Differences
- Classical Probability: Utilizes a defined sample space with ideal conditions.
- Empirical Probability: Relies on observed data, which may vary.
Practical Examples
- Julia's survey on presidential satisfaction yielded a probability of the next person being satisfied as 17/35 based on her collected data.
- Georgina's research on car ownership revealed a probability of the next respondent having no car as 35/61.
- Jill's coin flips gave her a probability of 2/3 for heads on the next flip based on previous results.
- Kiara's actual probability of flipping heads remains 1/2, assuming a fair coin.
Conclusion
- Understanding the distinction between empirical, subjective, and classical probability is crucial for accurately assessing probabilities in various situations.
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Description
Explore the concepts of classical, empirical, and subjective probability with these flashcards. Each card provides a clear definition along with relevant formulas. Perfect for students looking to enhance their understanding of probability terminology.
