1) Given that the sum of all probabilities must be equal to 1, and there are 6 plums, 14 clementines, and 12 nectarines we can tell there are 14+12+6 objects:
14+12+6= 32 this is our subspace.
2) So let's find first the probability of that teacher picking a nectarine:
[tex]{\textcolor{orange}{P(nectarine)}}=\frac{12}{32}[/tex]But notice, we don't want to know that we want the probability of not picking a nectarine so let's subtract that from 1 and write it this way:
3) We want to find the probability of the Complementary set to that:
[tex]\begin{gathered} {\textcolor{red}{P(NOT\: nectarine)}}=1-\frac{12}{32} \\ {\textcolor{red}{P(NOT\: nectarine)}}=\frac{32}{32}-\frac{12}{32} \\ {\textcolor{red}{P(NOTnectarine)}}=\frac{20}{32}=\frac{5}{8} \end{gathered}[/tex]Note that we simplified this.
