Question

Tags are placed to the left leg and right leg of a bear in a forest. Let A1 be the event that the left leg tag is lost and A2 the event that the right leg tag is lost. Suppose these two events are independent and P(A1)=P(A2)=.4. Find the probability that exactly one tag is lost, given that at least one tag is lost.

Answer 1

Answer: 0.51

Explanation:

Since A1 and A2 are independent so

P(A1 and A2) = P(A1)P(A2) = 0.3*0.3 = 0.09

By the addition rule, the probability that at least one leg tag is lost is

P(A1 or A2) = P(A1) + P(A2) - P(A1 and A2) = 0.3+0.3-0.09 = 0.51