A traffic light follows the pattern green, yellow, red for 55, 5, and 20 seconds, respectively. What is the probability that the driver approaching this light will find it green or yellow?
Total = 55 + 5 + 20 = 80
P( green) + P( yellow) - P(green and yellow)
( 55 + 5)/80 -0
P = 60/80 = .75
Well, let's do some math with a touch of humor, shall we? The total cycle time of the traffic light is 55 + 5 + 20 = 80 seconds. Now, if we want to find the probability of the light being green or yellow, we need to add up the times for green and yellow and divide by the total cycle time. So, we have 55 + 5 = 60 seconds for green and yellow. Dividing that by 80 gives us a probability of 60/80, which simplifies to 3/4. So, the probability that the driver will find the light green or yellow is 3 out of 4, or, in other words, 75%. Let's hope they catch it on a good day and don't end up stuck at the red light, contemplating the meaning of life.
To find the probability that the driver approaching the traffic light will find it green or yellow, we need to determine the total time the light is green or yellow compared to the total time it takes for one full cycle of the traffic light.
The total time for one full cycle is the sum of the times for green, yellow, and red:
Total time = green time + yellow time + red time = 55 + 5 + 20 = 80 seconds.
The total time for green or yellow is the sum of the times for green and yellow:
Green or yellow time = green time + yellow time = 55 + 5 = 60 seconds.
Finally, we can calculate the probability as the ratio of the time for green or yellow to the total time:
Probability = (Green or yellow time) / (Total time) = 60 / 80 = 0.75.
Therefore, the probability that the driver approaching this traffic light will find it green or yellow is 0.75 or 75%.
To find the probability that the driver approaching the traffic light will find it green or yellow, we need to calculate the total time that the light is green or yellow and divide it by the total time for one complete cycle of the traffic light.
The total time for one complete cycle of the traffic light can be calculated by summing the durations of each color: 55 seconds (green) + 5 seconds (yellow) + 20 seconds (red) = 80 seconds.
The total time that the light is green or yellow is the sum of the durations of the green and yellow lights: 55 seconds (green) + 5 seconds (yellow) = 60 seconds.
Now, we can calculate the probability by dividing the total time that the light is green or yellow by the total time for one complete cycle:
Probability = (Time for green or yellow) / (Total time for one complete cycle) = 60 seconds / 80 seconds = 0.75
Therefore, the probability that the driver approaching this traffic light will find it green or yellow is 0.75, or 75%.