83. 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 p  P(C1)  P(C2), and assume C1 and C2 are independent events. Derive an expression

(involving p) for the probability that exactly one tag is lost given that at most one is lost ( Ear Tag Loss in Red Foxes, J. Wildlife Manag., 1976:

164—167). (Hint: Draw a tree diagram in which the two initial branches refer to whether the left ear tag was lost.)