A traffic light runs repeatedly through the following cycle: green for 30 seconds, then yellow for 3 seconds, and then red for 30 seconds. Leah picks a random

If gonna let x= the current second of the the cycle that you start watching at at a total of x=63 cycles.

The only times that you will witness a colour change is when:

x=29: G, G, Y

x=30: G, Y, Y

x=32: Y,Y,R

x=33: Y,R,R

x=62: R,R,G

x=63: R,G,G.

There are 6/63 situations where you could witness a colour change therefore the probability is 6/63 or 0.0952

The overall cycle period is 63 seconds.  Leah has to choose any time in the 3 seconds before the green changes, or 3 seconds before the yellow changes or 3 seconds before the red changes.  That's a total of 9 seconds out of 63, so the probability of observing a color change is 9/63 = 1/7

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