Assignment II Due date: 11:59 PM EST 6/7/2022 You are expected to provide a clear and readable answer. To receive full credit your answer should include: Necessary and appropriate assumptions (when applicable) Formulas Show all your work Submit as a single PDF file. Make sure to pay attention to the due date. If you email your assignment to me after the due date and prior to Wednesday 6/8/2022 at 11:59 pm EST, it will be accepted, but there will be a 10% reduction to the assignment grade. Any later submission will not be allowed. 1. Risk of a natural gas pipeline accident. Process Safety Progress (December 2004) published a risk analysis for a natural gas pipeline between Bolivia and Brazil. The most likely scenario for an accident would be natural gas leak- age from a hole in the pipeline. The probability that the leak ignites immediately (causing a jet fire) is .01. If the leak does not immediately ignite, it may result in a delayed ignition of a gas cloud. Given no immediate ignition, the probability of delayed ignition (causing a flash fire) is .01. If there is no delayed ignition, the gas cloud will harmlessly disperse. Suppose a leak occurs in the natural gas pipeline. Find the probability that either a jet fire or a flash fire will occur. Illustrate with a tree diagram. 2. The airline industry defines an on-time flight as one that arrives within 15 minutes of its scheduled time. The recent arrival data for a small airport shows that 700 out of 1000 flight were on-time. There are three airlines operates from the airport, Airline A had 320 flights, Airline B had 440 flights and the remainder was operated by Airline C. Suppose that 75%% of Airline A's flights are on-time, and 65% of Airline B's flights are on-time. a. If four flights are selected at random, list the sample space indicating the possible arrival status (on-time "O" Late "L"). b. What is the probability that a randomly selected flight was from Airline A and was on time? What is the probability that a randomly selected flight was from Airline C or was on time? Given that the flight was late, what is the probability that it was from Airline B? Given that the flight was from Airline A, what is the probability that it was late