To find the probability we need to start by defining the event,
[tex]\text{event}=\text{ coin is not a dime}[/tex]then we find the possible outcomes, if the coin is not a dime it can be a quarter or a nickel.
then we find the possible outcomes
[tex]6+3=9[/tex]and the total outcomes
[tex]6+5+3=14[/tex]then the probability is going to be
[tex]\frac{9}{14}[/tex]