The feature space consists of three possible points (events) A, B, C, which occur with probability 0.2, 0.3, 0.5, respectively. For each event there are two possible labels +1 or −1, which happen with probability 0.9, 0.3 and 0.8 respectively (that is, P(1|A) = 0.9, P(1|B) = 0.3, P(1|C) = 0.8).

A) Determine the Bayes optimal classifier.

B) What is the expected loss of the Bayes optimal classifier?