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]
  • A

    $[0.36,0.40]$

  • B

    $[0.35,0.36]$

  • C

    $[0.25,0.35]$

  • D

    $[0.20,0.25]$

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