I meant “The ‘correct’ answer when you’re taking a probability class or are taking part in a study examining gambling fallacies and don’t want to be counted as one of the people who ‘clearly’ doesn’t understand probabilities.”
That said, I actually had a decent probability and statistics coursework instructor who would have marked “~100%” correct if a decent explanation were provided for the answer. (I answered problems that way all the time, although I don’t think that exact question turned up in any tests even though it did turn up in the probability textbook.)
I never took any test with that question with “a coin 100 times”, but I did have one with red/black on a roulette wheel (which I assume would be much harder to fudge than a coin) ten (IIRC) times. (And I answered 18⁄37 -- the zero is neither black nor red).
You forgot the 00, although it depends on whether you’re playing European or US roulette.
Actually, I love roulette. And yes, it’s much harder to fudge than a coin; the best that can be managed would be better described as a “nudge”—the timing of the dealer’s throw can make a tiny % of difference.
The skill necessary to land the ball exactly where the dealer wants it would be superhuman, but as my dad commented (describing practicing with throwing knives and throwing stars), practice has a tendency to make you luckier. (Yes, my homeschooling lessons involved throwing knives.)
If I understand correctly what he meant by “a probability problem”, your prior that the coin is biased is 0.
I meant “The ‘correct’ answer when you’re taking a probability class or are taking part in a study examining gambling fallacies and don’t want to be counted as one of the people who ‘clearly’ doesn’t understand probabilities.”
That said, I actually had a decent probability and statistics coursework instructor who would have marked “~100%” correct if a decent explanation were provided for the answer. (I answered problems that way all the time, although I don’t think that exact question turned up in any tests even though it did turn up in the probability textbook.)
I never took any test with that question with “a coin 100 times”, but I did have one with red/black on a roulette wheel (which I assume would be much harder to fudge than a coin) ten (IIRC) times. (And I answered 18⁄37 -- the zero is neither black nor red).
You forgot the 00, although it depends on whether you’re playing European or US roulette.
Actually, I love roulette. And yes, it’s much harder to fudge than a coin; the best that can be managed would be better described as a “nudge”—the timing of the dealer’s throw can make a tiny % of difference.
The skill necessary to land the ball exactly where the dealer wants it would be superhuman, but as my dad commented (describing practicing with throwing knives and throwing stars), practice has a tendency to make you luckier. (Yes, my homeschooling lessons involved throwing knives.)