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?

(Round to 3 decimal places)]

Answer 1

To find the probability that the employee is not late for work, we need to consider the probabilities of being stopped by each traffic light and calculate the overall probability.

Let's denote the events as follows:

A: Stopped by traffic light A

B: Stopped by traffic light B

C: Stopped by traffic light C

The given table provides the probabilities for each event:

P(A) = 0.3 (30% chance of being stopped by traffic light A)

P(B) = 0.4 (40% chance of being stopped by traffic light B)

P(C) = 0.2 (20% chance of being stopped by traffic light C)

To calculate the probability that the employee is not late for work, we need to find the complement of being late, which is the probability of not being stopped by any of the traffic lights.

The probability of not being stopped by a specific traffic light can be found by subtracting its probability of being stopped from 1:

P(not A) = 1 - P(A) = 1 - 0.3 = 0.7 (70% chance of not being stopped by traffic light A)

P(not B) = 1 - P(B) = 1 - 0.4 = 0.6 (60% chance of not being stopped by traffic light B)

P(not C) = 1 - P(C) = 1 - 0.2 = 0.8 (80% chance of not being stopped by traffic light C)

Since the events of being stopped or not stopped by each traffic light are independent, we can multiply the probabilities together to find the overall probability of not being stopped by any of the traffic lights:

P(not stopped by any traffic light) = P(not A) * P(not B) * P(not C)

= 0.7 * 0.6 * 0.8

= 0.336

Therefore, the probability that the employee is not late for work is 0.336 (or 33.6%).

Please note that this calculation assumes that the employee's arrival time at each traffic light is independent and does not take into account other factors such as traffic density or variations in the duration of being stopped at each traffic light.

Explanation:

Hope this helps have a good day!