Assume startups fail 90% of the time. 50% of the time your coin comes up tails, and you claim the startup will fail. 50% of the time your coin comes up heads and you claim the startup will succeed.
You guess correctly 0.5 (the chance your coin comes up tails) * 0.9 (the chance the startup fails) + 0.5 (heads) * 0.1 (success) = 0.5 of the time.
Assume startups fail 90% of the time. 50% of the time your coin comes up tails, and you claim the startup will fail. 50% of the time your coin comes up heads and you claim the startup will succeed.
You guess correctly 0.5 (the chance your coin comes up tails) * 0.9 (the chance the startup fails) + 0.5 (heads) * 0.1 (success) = 0.5 of the time.