A TRAFFIC LIGHT IS RED FOR 38 SECONDS YELLOW FOR 10 SECONDS AND GREEN FOR ONE MINUTE AND TWELVE SEONDS. IN A CONSTANTLY REPEATING CYCLE, WHAT IS THE PROBABILITY THAT AT THE MOMENT A PASSING PEDESTRIAN GLANCES AT IT, THE LIGHT WILL BE GREEN
Well, the light is green for a total of 72 seconds. There are 120 seconds in one complete cycle. You want to know the probability that it will be green, so you take the number of green seconds divided by the total number of seconds. 72/120= 3/5
the probability is 3/5
To calculate the probability that a passing pedestrian will glance at the traffic light when it is green, we need to consider the time intervals for each color.
Step 1: Calculate the total time for one complete cycle of the traffic light.
The total time for one complete cycle can be calculated by adding the durations of each color:
Total time = Red duration + Yellow duration + Green duration.
Red duration = 38 seconds
Yellow duration = 10 seconds
Green duration = 1 minute and 12 seconds = 60 seconds + 12 seconds = 72 seconds.
Total time = 38 seconds + 10 seconds + 72 seconds = 120 seconds.
Step 2: Calculate the probability of the light being green when a pedestrian glances at it.
The probability of the light being green when a pedestrian glances at it can be calculated by dividing the duration of the green light by the total time for one complete cycle.
Probability = Green duration / Total time.
Probability = 72 seconds / 120 seconds.
Simplifying the fraction, the probability is:
Probability = 3/5 or 0.6 (60%).
Therefore, the probability that, at the moment a passing pedestrian glances at the traffic light, it will be green is 0.6 or 60%.