Question

Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light.

What is the probability that the employee is not late for work?



Trafic light A P(A) 0.6
Trafic light B P(B) 0.4
Trafic light C P(C) 0.9

Answer 1

To find the probability that the employee is not late for work, you need to calculate the probability that he is not stopped by any of the traffic lights. The probability can be calculated by multiplying the probabilities of not being stopped by each individual light. In this case, the probability is 0.024.

Step-by-step explanation:

To find the probability that the employee is not late for work, we need to calculate the probability that he is not stopped by any of the traffic lights. Since the probabilities of being stopped by each traffic light are independent, we can calculate the probability that he is not stopped by each light and multiply them together.

The probability of not being stopped by Traffic light A is 1 - P(A) = 1 - 0.6 = 0.4. Similarly, the probabilities of not being stopped by Traffic lights B and C are 1 - P(B) = 1 - 0.4 = 0.6 and 1 - P(C) = 1 - 0.9 = 0.1, respectively.

To find the probability of not being stopped by any of the traffic lights, we multiply these probabilities together: P(not stopped by any light) = P(not stopped by A) * P(not stopped by B) * P(not stopped by C) = 0.4 * 0.6 * 0.1 = 0.024.