easy Probability

Probability of Unfair Coin I

A release-checked easy problem for training Conditional Probability.

Question

You have a pile of $100$ coins. $1$ of the coins is an unfair coin and has heads on both sides. The remaining $99$ coins are fair coins. You randomly select a coin from the pile and flip it $10$ times. The coin lands heads all $10$ times. Calculate the probability that the coin you selected is the unfair 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.