Question

traffic engineers are investigating the high rate of fatal accidents at a lighted city intersection. they discover that 23% 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).

Explanation:

Step1: Calculate the probability of a car stopping

The probability of a car passing through the red light \(p = 0.23\). The probability of a car stopping \(q=1 - p=1 - 0.23 = 0.77\)

Step2: Calculate the probability that both cars stop

Since the events are independent, the probability that both cars stop is \(q\times q=(0.77)\times(0.77)=0.5929\)

Step3: Calculate the probability that at least one car does not stop

The probability that at least one car does not stop (passes through the red - light) is \(P(X\geq1)=1 - P(X = 0)\)

Substitute \(P(X = 0)=0.5929\) into the formula, we get \(P(X\geq1)=1-0.5929 = 0.4071\)

Answer:

\(0.4071\)