This is a short article on conditional independence although the term conditional recurrence is used as the title. Basically, the article explores the difference between tossing a coin with a deterministic probability of heads versus tossing a coin with a random probability of heads. More specifically, the article considers the problem of choosing a coin at random from a box with two coins with different probabilities of heads, and then tossing the chosen coin. The tosses are conditionally independent given the type of coin, but dependent without this information.