1. Exercises on Discrete distributions

2. A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 2 of the next 5 vehicles are from out of state?

3. Suppose that a computer programmer, on average, makes 3 errors in 500 lines of code. What is the probability that the programmer will make no errors in 250 lines of code?

4. Six is the average number of oil tankers arriving each day at a certain port city. The facilities can handle at most 10 tankers per day. What is the probability that on a given day, some tankers will have to be turned away?

5. An Air Force intercept squadron consists of 16 planes that should always be ready for immediate launch. However, there is a probability of 0.25 that the engine of each plane will not start at a given attempt. If this happens, the mechanics must wait 5 minutes before trying to start the engine again. What is the expected number of planes to immediately launch?

6. The number of cracks in a section of interstate highway averages 2 per mile.
What is the probability that there will be at least 1 crack in the next ½ mile of the highway?

7. A particularly long traffic light on your way to work in the morning is green 20% of the time that you approach it. Over 20 mornings, what is the probability that the light is green on exactly 4 days?