Traffic engineers are investigating the high rate of fatal accidents at a lighted city intersection.
They discover that 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 both drivers pass through the red light without
stopping? (Please do not round your answer).

Question

Traffic engineers are investigating the high rate of fatal accidents at a lighted city intersection.
They discover that

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 both drivers pass through the red light without
stopping? (Please do not round your answer).

UpStudy AI · Accepted Answer

**Step 1: Identify the probability for one driver**

The probability that one driver passes through the red light is given as  
$$
P(\text{red light pass}) = 0.09.
$$

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**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:
$$
P(\text{both pass}) = P(\text{driver 1 passes}) \times P(\text{driver 2 passes}) = 0.09 \times 0.09.
$$

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**Step 3: Compute the joint probability**

$$
0.09 \times 0.09 = 0.0081.
$$

---

**Final Answer**

The probability that both drivers pass through the red light without stopping is  
$$
0.0081.
$$
The probability that both drivers pass through the red light without stopping is 0.0081.

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