There are some counters in a bag 5 red 6 blue and 1 green. Work out the probability that Jim picks out a counter that is not red?

There are some counters in a bag 5 red 6 blue and 1 green. Work out the probability that Jim picks out a counter that is not red ?

$$\textcolor[rgb]{150,0,0}{ 5 ~ \rm{red} } ~ bags
+\textcolor[rgb]{0,0,150}{ 6 ~ \rm{blue} } ~ bags
+\textcolor[rgb]{0,150,0}{ 1 ~ \rm{green} } ~ bag
= 12 ~ bags$$

The probability that Jim picks out a counter that is not red is:

$$\small{\text{$
\begin{array}{l}
\dfrac
{
\begin{pmatrix} \textcolor[rgb]{150,0,0}{r}
\\ 0 \end{pmatrix}\cdot
\begin{pmatrix} \textcolor[rgb]{0,0,150}{b}
\\ 1 \end{pmatrix}\cdot
\begin{pmatrix} \textcolor[rgb]{0,150,0}{g} \\ 0 \end{pmatrix}
+
\begin{pmatrix} \textcolor[rgb]{150,0,0}{r}
\\ 0 \end{pmatrix}\cdot
\begin{pmatrix} \textcolor[rgb]{0,0,150}{b}
\\ 0 \end{pmatrix}\cdot
\begin{pmatrix} \textcolor[rgb]{0,150,0}{g} \\ 1 \end{pmatrix}}
{
\begin{pmatrix} \textcolor[rgb]{150,0,0}{r}+
\textcolor[rgb]{0,0,150}{b}+
\textcolor[rgb]{0,150,0}{g} \\ 1 \end{pmatrix}
}\\\\
=
\dfrac
{
1 \cdot
\begin{pmatrix} \textcolor[rgb]{0,0,150}{b} \\ 1 \end{pmatrix}\cdot 1
+
1 \cdot 1 \cdot
\begin{pmatrix} \textcolor[rgb]{0,150,0}{g} \\ 1 \end{pmatrix}}
{
\begin{pmatrix} \textcolor[rgb]{150,0,0}{r}+
\textcolor[rgb]{0,0,150}{b}+
\textcolor[rgb]{0,150,0}{g} \\ 1 \end{pmatrix}
}\\\\
=
\dfrac
{
\begin{pmatrix} \textcolor[rgb]{0,0,150}{b} \\ 1 \end{pmatrix}+
\begin{pmatrix} \textcolor[rgb]{0,150,0}{g} \\ 1 \end{pmatrix}
}
{
\begin{pmatrix} \textcolor[rgb]{150,0,0}{r}+
\textcolor[rgb]{0,0,150}{b}+
\textcolor[rgb]{0,150,0}{g} \\ 1 \end{pmatrix}
}\\\\
=
\dfrac{ \textcolor[rgb]{0,0,150}{b}+
\textcolor[rgb]{0,150,0}{g} }{ \textcolor[rgb]{150,0,0}{r}+
\textcolor[rgb]{0,0,150}{b}+
\textcolor[rgb]{0,150,0}{g} } \\\\
=
\dfrac{ \textcolor[rgb]{0,0,150}{6}+
\textcolor[rgb]{0,150,0}{1} }{ \textcolor[rgb]{150,0,0}{5}+
\textcolor[rgb]{0,0,150}{6}+
\textcolor[rgb]{0,150,0}{1} } \\\\
=
\dfrac{ 7 }{ 12 }
\end{array}
$}}$$

Ther are 12 counters....7 are not red....so....the probability that a red one is not selected = 7/12

There are 12 total counters. You get 12 by doing 5+6+1. Take the amount of red counters and subtract it from the total number of counters by doing 12-5. Your answer is 7. Put that over the total, and the probability of Jim not picking a red counter is 7/12.

Hope this helps