Even heads with one fair coin
You have coins on the table. Exactly one of them is a fair coin; each of the other coins is biased and lands heads with probability , where (the biased coins need not share the same ). You flip all coins at once. What is the probability that the total number of heads is even?
Show hints (2)+
- Condition on everything except the fair coin. Once the biased coins are fixed, is the parity of their heads-count determined?
- A fair coin flips the running parity with probability exactly one half - so what does the final parity look like, no matter the rest?
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Asked at: Jane Street, SIG