a) Why do we care about probability theory in this class?
b) What does independence (as in “events are independent”) mean? Given a real-world example of events that are independent. Give an example of events that are not independent.
c) What is the difference between a combination and a permutation? Be precise.
d) Assume you roll two fair die (dice), what is the probability of rolling a pair (that is, a 1-1, 2-2, 3-3, etc.)?
e) Repeat (a) for three fair die and rolling a triple (that is, 1-1-1, 2-2-2, etc.).
f) Assume that a given Coke machine has a probability of 0.01 (1%) of taking your money and not giving you a drink. Assume that the event of stealing your money is independent of previous events. What is the probability that on Monday 3:00pm this Coke machine will steal your money? If it does steal you money at 3:00pm, what is the probability that it will steal your money on a second attempt to buy a drink at, say, 3:01pm?
g) Assume that the probability of a received message having an error is 0.10 (errors are independent). What is the probability of receiving 5 good (that is, error free) messages? What is the probability of receiving 4 messages such that 1 or more messages have an error?
h) What is a random variable?