Chapter 2.5, Problem 89E

Suppose identical tags are placed on both the left ear and the right ear of a fox. The fox is then let loose for a period of time. Consider the two events C₁ = {left ear tag is lost} and C₂ = {right ear tag is lost}. Let π = P(C₁) = P(C₂), and assume C₁ and C₂ are independent events. Derive an expression (involving π) for the probability that exactly one tag is lost, given that at most one is lost (“Ear Tag Loss in Red Foxes,” J. Wildlife Mgmt., 1976: 164–167). [Hint: Draw a tree diagram in which the two initial branches refer to whether the left ear tag was lost.]