89. 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 and

. Let , and assume C1 and C2 are independent events. Derive an expression

(involving ) 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.]

p 5 P(C1) 5 P(C2C2 5 5right ear tag is lost6 )

C1 5 5left ear tag is lost6 P(A2 |A3 )

P(A1 ´ A2 ´ A3) 5 .88 P(A2 ¨ A3P(A1 ´ A2 ) 5 .40 ) 5 .80 P(A3P(A2 ) 5 .70 P(A1 ) 5 .65 ) 5 .55