In the U.S., the EIT (Engineering In Training) is a professionaldesignation certifying engineers. Assume only four broad categoriesof engineers – chemical, electrical, mechanical, and civil. Arecent survey found that 20% of EIT test-takers were chemicalengineers,35% were electrical engineers, 30% were mechanicalengineers, and 15% were civil engineers. If a test-taker is achemical engineer, there is a 20% chance they fail the test. If atest-taker is an electrical engineer, there is a 15% chance theyfail the test. Similarly, if a test-taker is a mechanical or civilengineer, there is a 10% and 25% chance of failing,respectively.

a)What is the probability that a randomly selected test-taker isa chemical engineer and failed the test?

b)What is the probability that a randomly selected test-takerfailed the test?

c)If a randomly selected test-taker is a chemical engineer, whatis the probability that they failed the test?

d)If a randomly selected test-taker failed the test, what is theprobability they are a chemical engineer?