Questions / Quant trading, Information & Bayes
A shared hidden success rate
A fair coin secretly chooses a success probability of 0.2 or 0.8. Two trials are independent conditional on that chosen probability. What is the probability that both succeed? Enter a percentage.
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Answer: 34% (17/50)
- The two-success likelihoods are 0.2² and 0.8². Their average is (0.04 + 0.64)/2 = 0.34, which exceeds the product of the marginal success rates.
Interview shortcut. Average the two-success probabilities: (0.2² + 0.8²)/2, not 0.5².
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.