Chapter 5, Problem 125CRE

Red Light/Green Light A busy street has three traffic lights in a row. These lights are not synchronized, so they run independently of each other. At any given moment, the probability that a light is green is 60%. Assuming that there is no traffic, follow the steps below to design a simulation to estimate the probability that you will get three green lights.

a. Identify the action with a random outcome, and give the probability that it is a success.

b. Explain how you will simulate this action using the random number table in Appendix

A. Which digits will represent green, and which non-green? If you want to get the same results we did, use all the possible one-digit numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), and let the first few represent the green lights. How many and what numbers would represent green lights, and what numbers would represent nongreen lights?

c. Describe the event of interest.

d. Explain how you will simulate a single trial.

e. Carry out 20 repetitions of your trial, beginning with the first digit on line 11 of the random number table. For each trial, list the random digits, the outcomes they represent, and whether or not the event of interest happened.

f. What is the empirical probability that you get three green lights?