$\text{ The probabilities of three events }\mathrm{A},\mathrm{B}\text{ and }\mathrm{C}\text{ are given by }P\left(A\right)=0.6,P\left(B\right)=0.4\text{ and }$

$P\left(C\right)=0.5.\text{ If }P(A\cup B)=0.8,P(A\cap C)=0.3,P(A\cap B\cap C)=0.2,P(B\cap C)=\beta \text{ and }$

$P(A\cup B\cup C)=\alpha \text{ where }0.85\le \alpha \le 0.95,\text{ then }\beta \text{ lies in the interval : }$

• A

  $\left[0.20,0.25\right]$

• B

  $\left[0.25,0.35\right]$

• C

  $\left[0.35,0.36\right]$

• D

  $\left[0.36,0.40\right]$