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Here's a hint: Is the probability of Alice winning the C-A-A vs. C-B race different from the probability of Alice winning the C-A vs. C-B race?
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Here's a hint: Is the probability of Alice winning the C-A-A vs. C-B race different from the probability of Alice winning the C-A vs. C-B race?
There is a small mistake in (b). If x approaches 0.5, your solution would imply that Alice wins with near 100% probability.