My Courses CRN 40938 Chapter 3 HW- Probability Topics Current score: \( { }^{+} \)Ảl. Category: Homework 90.39/100 points c. What is the probability that a person selected at random is either administration or against increasing the fees? \[ \frac{1733}{2504} \] d. What is the probability that a person selected at random is in favor of increasing the fees and is against increasing the fees? \[ 0 \] e. What is the probability that a faculty member selected at random is against increasing the fees? \[ 0.279 \]

Did you know that probability has roots dating back to ancient civilizations? The earliest recorded studies of probability can be traced to the games of chance played by the Romans and the dice of the Greeks. However, it wasn't until the 17th century that the mathematical foundations of probability were formalized by notable figures like Blaise Pascal and Pierre de Fermat, who explored the mathematical nuances behind poker bets. When dealing with probabilities, it's easy to trip over common misconceptions. One classic mistake is assuming that outcomes are independent when they are not. For example, if you consider a question like the one about being "in favor" and "against" fee increases, it’s important to remember that you can’t be both at the same time, hence the probability of selecting someone who is both is zero! Keep your definitions clear!