The probability of an event is expressed as
[tex]Pr(\text{event) =}\frac{Total\text{ number of favourable/desired outcome}}{Tota\text{l number of possible outcome}}[/tex]
Given:
[tex]\begin{gathered} \text{Red}\Rightarrow2 \\ \text{Green}\Rightarrow3 \\ \text{Blue}\Rightarrow2 \\ \Rightarrow Total\text{ number of balls = 2+3+2=7 balls} \end{gathered}[/tex]
The probability of drwing two blue balls one after the other is expressed as
[tex]Pr(\text{blue)}\times Pr(blue)[/tex]
For the first draw:
[tex]\begin{gathered} Pr(\text{blue) = }\frac{number\text{ of blue balls}}{total\text{ number of balls}} \\ =\frac{2}{7} \end{gathered}[/tex]
For the second draw, we have only 1 blue ball left out of a total of 6 balls (since a blue ball with drawn earlier).
Thus,
[tex]\begin{gathered} Pr(\text{blue)}=\frac{number\text{ of blue balls left}}{total\text{ number of balls left}} \\ =\frac{1}{6} \end{gathered}[/tex]
The probability of drawing two blue balls one after the other is evaluted as
[tex]\begin{gathered} \frac{1}{6}\times\frac{2}{7} \\ =\frac{1}{21} \end{gathered}[/tex]
The probablity that none of the balls drawn is blue is evaluted as
[tex]\begin{gathered} 1-\frac{1}{21} \\ =\frac{20}{21} \end{gathered}[/tex]
Hence, the probablity that none of the balls drawn is blue is evaluted as
[tex]\frac{20}{21}[/tex]
