Dr. six drives through two stoplights on her way to work. the first light is green for 20 seconds out of each minute. the second light is green for 35 seconds out of each minute. what is the probability that dr. six will hit two green lights?

Probability 1 * Probability 2 = Probability of both

Let minute = 60 seconds

First light probability = 20/60 (20 seconds out of each 60 seconds)
= 0.33 (recurring)

Second light probability = 35/60 (35 seconds out of each 60 seconds)
= 0.5833 (recurring)

To get a more accurate end probability use the numbers 20/60 and 35/60 appose to the rounding (on the calculator):

Using the formula at the top:
20/60 * 35/60 = 0.194  (3 DP) 

The probability of that Dr. Six will hit two green lights is 0.194 (3DP)