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