1.
Let AA, BB and CC be three events such that the probability that exactly one of AA and BB occurs is (1k)(1 - k), the probability that exactly one of BB and CC occurs is (12k)(1 - 2k), the probability that exactly one of CC and AA occurs is (1k)(1 - k) and the probability of all AA, BB and CC occurring simultaneously is k2k^2, where 0<k<10 < k < 1. Then the probability that at least one of AA, BB and CC occurs is: