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 \(…

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 \( P(A \cup B)=0.8, P(A \cap C)=0.3, P(A \cap B \cap C)=0.2 \), \( P(B \cap C)=\beta \) and \( P(A \cup B \cup C)=\alpha \), where \( 0.85 \leq \alpha \leq 0.95 \), then \( \beta \) lies in the interval

[JEE Main 2020, 6 Sep (Shift 2)]