The probabilities of three events $\mathrm{A}, \mathrm{B}$ and C are given by $\mathrm{P}(\mathrm{A})=0.6, \mathrm{P}(\mathrm{B})=0.4$ and $\mathrm{P}(\mathrm{C})=0.5$. If $\mathrm{P}(\mathrm{A} \cup \mathrm{B})=0.8, \mathrm{P}(\mathrm{A} \cap \mathrm{C})=0.3, \mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=0.2$, $P(B \cap C)=\beta$ and $P(A \cup B \cup C)=\alpha$, where $0.85 \leq \alpha \leq$ 0.95 , then $\beta$ lies in the interval :
