Chapter 6 Quiz: Probability Intuition
Q1. A coin lands heads 8 times in a row. What is the probability it lands heads on the 9th flip?
a) Less than 50% — it should balance out b) More than 50% — streaks tend to continue c) Exactly 50% — each flip is independent d) Can't know without more information
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**c) Exactly 50%** A fair coin has no memory. Each flip is an independent event. The probability of heads is always 0.5 regardless of history. Answering (a) is the gambler's fallacy; answering (b) is the hot hand fallacy.Q2. The frequentist interpretation of probability defines probability as:
a) How much you believe an event will occur b) The long-run frequency of an event over many repeated trials c) The number of favorable outcomes divided by total outcomes d) A subjective confidence level
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**b) The long-run frequency of an event over many repeated trials** The frequentist interpretation grounds probability in observable frequencies over repetition. Option (c) describes a subset of the frequentist approach (classical probability with equal outcomes), but isn't the full definition. Option (a) and (d) describe the Bayesian interpretation.Q3. A disease affects 1 in 1,000 people. A test for it is 99% accurate (1% false positive rate). You test positive. Approximately what is the probability you actually have the disease?
a) ~99% b) ~50% c) ~9% d) ~1%
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**c) ~9%** In 1,000 people: ~1 true positive, ~10 false positives (1% of 999). Of ~11 positives, only ~1 actually has the disease ≈ 9%. The low base rate (1 in 1,000) overwhelms the high test accuracy. This is the base rate neglect problem.Q4. Two events are independent if:
a) They can't both occur at the same time b) Knowing the outcome of one tells you nothing about the other c) They're both equally probable d) They're separated by significant time
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**b) Knowing the outcome of one tells you nothing about the other** Independence means the conditional probability P(A|B) equals the unconditional probability P(A) — knowing B happened doesn't change the probability of A.Q5. The probability that events A AND B both occur (when they are independent) equals:
a) P(A) + P(B) b) P(A) × P(B) c) P(A|B) d) P(A) + P(B) - P(A and B)
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**b) P(A) × P(B)** For independent events, the multiplication rule gives the probability of both occurring. Option (a) is the addition rule for mutually exclusive events. Option (d) is the general addition rule for overlapping events.Q6. Nadia finds that videos she posts on Tuesdays get more views than on other days, based on 4 weeks of data. This pattern is best described as:
a) Statistically significant b) Likely spurious, given the small sample size and high variance of social media metrics c) Definitive evidence that Tuesday is her best posting day d) Evidence of algorithmic favoritism for Tuesday posts
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**b) Likely spurious, given the small sample size and high variance of social media metrics** With only 4 data points per day, extremely high variance in view counts, and the multiple comparisons problem (checking 7 days creates 7 chances to find a spurious pattern), a Tuesday pattern is far more likely to be noise than signal.Q7. True or False: A psychic who predicts 10 events correctly in a row has demonstrated genuine psychic ability.
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**False.** To evaluate this, you'd need to know: How many total predictions did they make? How many opportunities were there? If they made 100 predictions and got 10 right, that's not impressive. If they made 10 predictions and got all 10 right on specific, unambiguous claims, that would be more interesting — but you'd still need to consider whether the predictions were genuinely precise (not vague Barnum statements), whether they were made before the events (not retrofitted), and what the base rate was for each prediction being correct by chance.Q8. Short answer: What is conditional probability, and give one real-world example where thinking conditionally would change your probability estimate?