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Let's say I flipped two coins. I tell you I did this. You ask me, "Did heads come up at least once?" I answer yes. What are the odds that the other coin was ta
by function_seven 8y ago
Let's say I flipped two coins. I tell you I did this. You ask me, "Did heads come up at least once?" I answer yes.
What are the odds that the other coin was tails? 2/3, because there are three scenarios (HH, HT, TH) that satisfy my first answer to you.
If you flip a pair of coins a few thousand times, and search the flip pairs for all the ones that had a heads among them, you'll find a tails in those pairs 2/3 of the time, and a pair of heads 1/3 of the time.
Same with the girl-boy problem.
Now if you ask me if the left coin came up heads—and I say yes—that doesn't give you any information whatsoever on the right coin. And if you search through the thousands of pair flips looking for an "H" in the left column, the right column will 50/50 have an H or a T.
- titzer 8y agoThat's a good explanation. > Now if you ask me if the left coin came up heads—and I say yes—that doesn't give you any information whatsoever on the right coin. Exactly. "At least one" gives information about the whole set, implicitly giving information about the second one whereas "the first one is X" gives no information about the second one.