Of the 50 students in an undergraduate statistics class, 60% send email and/or text messages during any given lecture. They have
a 50/50 chance of being caught by their professor, who is not amused by such unprofessional conduct. The eagle-eyed professor never charges an innocent student. What is the probability a student sends an email and/or text message during lecture and gets caught?
Since no innocent student will ever be caught, the probability that a student sends an email and/or text message during a lecture AND gets caught is given by the product of the probability of a student sending a message (60%) by the probability of the professor catching them (50%) :
