Final answer:
To find the probability that at least one of two drivers runs a red light, calculate the probability that neither runs it (0.64) and subtract from 1, resulting in a 36% chance that at least one driver will pass through on red.
Step-by-step explanation:
To calculate the probability that at least one of the drivers passes through the red light without stopping, we use the complement rule. This approach involves finding the probability that neither driver runs the red light and subtracting that probability from 1. Given the probability of a car running the red light is 0.20 (20%), the probability of a car not running the red light is 1 - 0.20 = 0.80 (80%).
Since the two drivers behave independently, we find the joint probability of both cars not running the light by multiplying their individual probabilities:
Probability that neither driver runs the red light = 0.80 (Car 1 not running red light) × 0.80 (Car 2 not running red light) = 0.64.
We then subtract this joint probability from 1 to find the probability that at least one driver runs the red light:
Probability that at least one driver runs the red light = 1 - Probability that neither driver runs the red light = 1 - 0.64 = 0.36.
Therefore, there is a 0.36 (or 36%) probability that at least one of the two drivers will run the red light when they are within 200 feet of the intersection as the light turns red.
The Question is incomplete. The complete question is
Traffic engineers are investigating the high rate of fatal accidents at a lighted city intersection. They discover that 20 % of the cars that are within 200 feet of the intersection when the light turns red pass through the red light without stopping. Suppose two cars are now within 200 feet of the intersection and the light turns red. Assuming that drivers behave independently of one another, What is the probability that at least one of the drivers passes through the red light without stopping? (Please do not round your answer).