given the Venn diagram above what is the probability that neither event A or B will occur

Conider that the probability that neither event A or B will occur is given by the formula,
[tex]P(A\cup B)^c=1-P(A\cup B)[/tex]Substitute the values,
[tex]P(A\cup B)^c=1-(0.3+0.2+0.1)=1-0.6=0.4[/tex]Thus, the required probability is 0.4