Counterintuitive Probability

Questions

1. 1
   Not answered. On what numeric scale is a probability always measured?
2. 2
   Not answered. A weather model says there is a 30% chance of rain tomorrow. What is the chance of no rain?
3. 3
   Not answered. When every outcome in the sample space is equally likely, how do you find the probability of an event?
4. 4
   Not answered. You roll two fair six-sided dice and add them. Which total is the most likely?
5. 5
   Not answered. Two events are independent. How do you find the probability that BOTH occur?
6. 6
   Not answered. For a single roll of a fair die, what is the probability of rolling a 1 or a 2?
7. 7
   Not answered. What does the conditional probability P(A | B) measure?
8. 8
   Not answered. What is the expected (average) value of a single roll of a fair six-sided die?
9. 9
   Not answered. Rolling one die four times, is getting at least one six more likely than not?
10. 10
    Not answered. A fair coin has landed heads five times in a row. What is the probability the next flip is heads?
11. 11
    Not answered. Which belief is the gambler's fallacy?
12. 12
    Not answered. Why does a streak of heads NOT make tails more likely on the very next flip?
13. 13
    Not answered. At the Monte Carlo Casino in 1913, the roulette ball reportedly landed on black 26 times in a row. What did this famously trigger?
14. 14
    Not answered. What does the law of large numbers actually promise about flipping a fair coin?
15. 15
    Not answered. As you keep flipping a fair coin, what happens to the raw gap between the number of heads and the number of tails?
16. 16
    Not answered. Someone walks in, sees you roll a double-six, and concludes 'you must have been rolling for a long time to finally get that.' What error is this?
17. 17
    Not answered. The gambler's fallacy expects a streak to reverse. Which belief expects a streak to continue?
18. 18
    Not answered. Monty Hall: behind three doors are a car and two goats. You pick a door; the host, who knows the layout, opens a different door revealing a goat, then offers you the switch. Should you switch?
19. 19
    Not answered. In the standard Monty Hall game, what crucial fact makes switching better than staying?
20. 20
    Not answered. The 2/3 switching advantage relies on specific rules. Which set of assumptions is required?
21. 21
    Not answered. Now imagine 100 doors. You pick one; the host opens 98 other doors, all goats, leaving a single door closed. Should you switch?
22. 22
    Not answered. Variant: the host forgets where the car is and opens one of the other two doors at random — and it happens to reveal a goat. Now should you switch?
23. 23
    Not answered. When Marilyn vos Savant published the switching answer in Parade magazine in 1990, how was it received?
24. 24
    Not answered. Where did the 'Monty Hall problem' first appear in print under that framing?
25. 25
    Not answered. How many people must be in a room before it is more likely than not that at least two share a birthday?
26. 26
    Not answered. Why does it take so few people (just 23) to make a shared birthday likely?
27. 27
    Not answered. What is the cleanest way to calculate the probability of at least one shared birthday?
28. 28
    Not answered. In a room of 70 people, roughly how likely is it that at least two share a birthday?
29. 29
    Not answered. Ignoring leap years (so 365 possible birthdays), how many people guarantee — with 100% certainty — that two of them share a birthday?
30. 30
    Not answered. How many OTHER people must be in a room before there is a better-than-even chance that someone shares YOUR specific birthday?
31. 31
    Not answered. Cryptography's 'birthday attack' uses this same paradox. Roughly how many random items must you generate to likely find a collision among N equally likely hash values?
32. 32
    Not answered. A disease affects 1% of people. A test is 99% accurate for both the sick and the healthy. You test positive. What is the chance you actually have the disease?
33. 33
    Not answered. Linda is 31, single, outspoken, and a former philosophy student deeply concerned with social justice. Which is more probable?
34. 34
    Not answered. What is Simpson's paradox?
35. 35
    Not answered. A family has two children. You learn that at least one is a boy (and nothing about birth order). Assuming boys and girls are equally likely and independent, what is the probability that both are boys?
36. 36
    Not answered. In many real-world datasets (populations, street addresses, financial figures), how often does the leading digit turn out to be 1?
37. 37
    Not answered. A game: flip a fair coin until it lands heads. If the first head appears on flip k, you win 2^k dollars. What is the expected payout?
38. 38
    Not answered. On an American roulette wheel (38 pockets), you bet $1 straight-up on a single number that pays 35 to 1. What is your long-run expected result per $1 bet?