Step 1 :Given that the total time for a cycle is 60 seconds, and the light is not green for $(60-25)=35$ seconds.
Step 2 :We are asked to find the probability that the light will not be green at a randomly chosen time. This can be calculated by dividing the time that the light is not green by the total cycle time.
Step 3 :Let's denote the time that the light is not green as \(not\_green\_time\) and the total cycle time as \(total\_cycle\_time\).
Step 4 :So, \(not\_green\_time = 35\) and \(total\_cycle\_time = 60\).
Step 5 :The probability that the light will not be green at a randomly chosen time is calculated as \(probability\_not\_green = \frac{not\_green\_time}{total\_cycle\_time}\).
Step 6 :Substituting the given values, we get \(probability\_not\_green = \frac{35}{60} = 0.5833333333333334\).
Step 7 :Final Answer: The probability that the light will not be green at a randomly chosen time is \(\boxed{0.583}\) or approximately 58.3%.