We know that:
[tex]\begin{gathered} P(A\cup B)^{\prime}=1-P(A\cup B) \\ P(A\cup B)^{\prime}=1-P(A)+P(B)-P(A\cap B) \end{gathered}[/tex]Plugging the values given we have that:
[tex]\begin{gathered} 0.15=1-0.8+0.75-P(A\cap B) \\ P(A\cap B)=1-0.8+0.75-0.15 \\ P(A\cap B)=0.8 \end{gathered}[/tex]Now, since the probability of the intersection is not zero this means that the events are non-mutually exclusive.
