The probabilities of three events A,B and C are given by P(A)=0.6,P(B)=0.4 and P(C)=0.5. If P(A∪B)=0.8,P(A∩C)=0.3,P(A∩B∩C)=0.2,P(B∩C)=β and P(A∪B∪C)=α where 0.85≤α≤0.95, then β lies in the interval :