Question
Traffic engineers are investigating the high rate of fatal accidents at a lighted city intersection.
They discover that
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 both drivers pass through the red light without
stopping? (Please do not round your answer).
They discover that
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 both drivers pass through the red light without
stopping? (Please do not round your answer).
Ask by Ingram Nichols. in the United States
Mar 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that both drivers pass through the red light without stopping is 0.0081.
Solution
Step 1: Identify the probability for one driver
The probability that one driver passes through the red light is given as
Step 2: Use the independence of driver behavior
Since the two drivers behave independently, the probability that both drivers pass through the red light is the product of their individual probabilities:
Step 3: Compute the joint probability
Final Answer
The probability that both drivers pass through the red light without stopping is
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To find the probability that both drivers pass through the red light without stopping, we can use the independence of the two events.
The probability that one car passes the light when it turns red is given as
Since the events are independent, we can multiply the probabilities of each event:
Calculating this gives:
Thus, the probability that both drivers pass through the red light without stopping is
