You have 100 coins, 99 fair and 1 double-headed. You pick a coin at random and flip it 10 times, getting heads each time. What is the probability you picked the double-headed coin?

You have 100 coins, 99 fair and 1 double-headed. You pick a coin at random and flip it 10 times, getting heads each time. What is the probability you picked the double-headed coin?

Approach: Use Bayes' theorem with prior probabilities.

P(double-headed|10 heads) = (1/100 * 1) / (1/100 * 1 + 99/100 * (1/2)^10) ≈ 0.9118

Follow-up: How many heads needed for probability > 0.99?

Key concepts: Bayes theorem, prior, posterior.