A, B, C are mutually exclusive and exhaustive events of a random experiment and E is an event that occurs in conjunction with one of the events A, B, C. The conditional probabilities of E given the happening of A, B, C are respectively 0.6, 0.3 and 0.1. If \( P(A) = 0.30 \) and \( P(B) = 0.50 \), then \( P(C \mid E) = \):