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Questions and Answers
According to Kerrich, what happens to the chance error (the difference between the number of heads and half the number of tosses) as the number of coin tosses increases?
According to Kerrich, what happens to the chance error (the difference between the number of heads and half the number of tosses) as the number of coin tosses increases?
- It tends to decrease in absolute terms.
- It decreases in absolute terms, but increases as a percentage of the total tosses.
- It tends to increase in absolute terms, but decreases as a percentage of the total tosses. (correct)
- It remains constant.
In Kerrich's coin-tossing experiment, what was the difference between the number of heads and half the number of tosses after 1,000 tosses?
In Kerrich's coin-tossing experiment, what was the difference between the number of heads and half the number of tosses after 1,000 tosses?
- 33
- 2 (correct)
- 67
- 5
What is the significance of the phrase "the roulette wheel has neither conscience nor memory" in the context of probability and the law of averages?
What is the significance of the phrase "the roulette wheel has neither conscience nor memory" in the context of probability and the law of averages?
- It emphasizes that the house always wins in the long run.
- It suggests that roulette wheels are rigged to give certain outcomes.
- It means that each spin of the roulette wheel is independent and unaffected by previous spins. (correct)
- It implies that past outcomes influence future probabilities in random events.
Kerrich states that after a run of four heads, the probability of getting a tail on the next toss is:
Kerrich states that after a run of four heads, the probability of getting a tail on the next toss is:
According to Kerrich, if one multiplies the number of tosses by 100, what happens to the likely size of the chance error?
According to Kerrich, if one multiplies the number of tosses by 100, what happens to the likely size of the chance error?
In the context of the law of averages, what does 'chance error' refer to?
In the context of the law of averages, what does 'chance error' refer to?
Which statement about the law of averages is most accurate, according to Kerrich?
Which statement about the law of averages is most accurate, according to Kerrich?
If Kerrich tossed a coin 100 times, approximately what size of chance error would he likely expect?
If Kerrich tossed a coin 100 times, approximately what size of chance error would he likely expect?
What was the main purpose of John Kerrich's coin-tossing experiment during World War II?
What was the main purpose of John Kerrich's coin-tossing experiment during World War II?
What is the correct formula, according to Kerrich?
What is the correct formula, according to Kerrich?
What common misconception about the law of averages did Kerrich address with his assistant?
What common misconception about the law of averages did Kerrich address with his assistant?
Based on Kerrich's findings, if someone tosses a coin 20,000 times, what can they expect regarding the chance error compared to 10,000 tosses?
Based on Kerrich's findings, if someone tosses a coin 20,000 times, what can they expect regarding the chance error compared to 10,000 tosses?
Why was Kerrich's coin-tossing experiment significant in understanding the law of averages?
Why was Kerrich's coin-tossing experiment significant in understanding the law of averages?
If a coin is tossed many times and the percentage of heads is slightly less than 50%, what does the law of averages suggest will happen as more tosses are performed?
If a coin is tossed many times and the percentage of heads is slightly less than 50%, what does the law of averages suggest will happen as more tosses are performed?
What is a practical implication of the law of averages in real-world scenarios?
What is a practical implication of the law of averages in real-world scenarios?
What does Kerrich mean when he says, "The number of heads will be around half the number of tosses, but it will be off by some amount—chance error."
What does Kerrich mean when he says, "The number of heads will be around half the number of tosses, but it will be off by some amount—chance error."
What is the role of the assistant in Kerrich's discussion?
What is the role of the assistant in Kerrich's discussion?
In the context of Kerrich's experiment, what is the key difference between the 'absolute' chance error and the 'relative' chance error?
In the context of Kerrich's experiment, what is the key difference between the 'absolute' chance error and the 'relative' chance error?
Why does Kerrich use the example of tossing a coin multiple times to explain the law of averages?
Why does Kerrich use the example of tossing a coin multiple times to explain the law of averages?
How does Kerrich use Table 1 and Figure 1 from his experiment to argue his point about the law of averages?
How does Kerrich use Table 1 and Figure 1 from his experiment to argue his point about the law of averages?
Flashcards
Chance of Heads
Chance of Heads
With a fair coin, the chance of getting heads remains at 50%, regardless of previous outcomes.
Chance Error
Chance Error
The difference between the observed number of heads and the expected number (half the number of tosses).
Chance Error Increase (Absolute)
Chance Error Increase (Absolute)
As the number of trials increases, the absolute size of the chance error tends to increase as well.
Chance Error Decrease (Relative)
Chance Error Decrease (Relative)
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Law of Averages Definition
Law of Averages Definition
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Chance Error Size
Chance Error Size
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Chance Error Scaling
Chance Error Scaling
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Study Notes
- The law of averages is commonly misunderstood to mean that after a series of heads in coin tosses, tails become more likely to even out the results.
- The chance of getting heads with a fair coin remains at 50%, regardless of previous outcomes.
Kerrich's Coin-Tossing Experiment
- John Kerrich, while interned during World War II, conducted an experiment involving 10,000 coin tosses.
- In 10,000 tosses, Kerrich got 5,067 heads, a difference of 67 from the expected 5,000.
- The "chance error" refers to the difference between the actual number of heads and the expected number (half the number of tosses).
Understanding Chance Error
- The equation is: number of heads = half the number of tosses + chance error.
- The absolute size of the chance error tends to increase as the number of tosses increases.
- However, relative to the number of tosses, the chance error decreases.
- For example, with 100 tosses, the chance error is likely to be around 5, but with 10,000 tosses, it's likely to be around 50.
- Multiplying the number of tosses by 100 multiplies the likely size of the chance error by approximately 10 (the square root of 100).
Key Takeaway
- As the number of tosses increases, the difference between the number of heads and half the number of tosses (chance error) gets larger.
- The difference between the percentage of heads and 50% gets smaller.
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