easy Probability

Confident Double Heads

A release-checked easy problem for training Conditional Probability.

Question

A bag has $19$ fair coins and one double-headed coin. We pick a coin uniformly at random from the bag. What is the minimum number of times this coin would need to appear heads in a row to be at least $95\%$ certain that the coin we have is the double-headed coin?

Practice focus

This Probability problem is tagged Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.