Assignment:
Suppose you are flying a four-engine aircraft on a 10-hour transoceanic flight. Assume that it has been established that the probability of an engine of the type you have on your aircraft failing during a 10-hour flight is 0.008. Determine the probability of all four engines failing during the flight.
A student decided that this is a binomial distribution problem. Remember that the four characteristics of a binomial distribution are:
- Fixed number of trials
- Two possible outcomes
- Fixed probability of success
- Independence of events
Evaluate the problem in terms of the four characteristics and explain whether you think it does or does not fit the characteristics of a binomial distribution. If not, which characteristics do not hold? Note that in determining whether or not a problem is "binomial" or not, you must evaluate it against the four characteristics listed above.
The student found that the probability of all four engines failing is 4.1E-09. Is that answer correct?
Provide complete and step by step solution for the question and show calculations and use formulas.