*Simple Probabilities* (**): Calculate the following probabilities:

- Drawing an ace from a deck of cards?
- Getting a number divisible by 3 after rolling a die?
- Sum of two dice being equal to 7?
- Getting at least one head after flipping a coin twice?

*Probability of a Union I* (*): Consider the two events *A* and *B* which are mutually exclusive. The probabilities associated with those two events are *Pr(A)=0.23* and *Pr(B)=0.47*. What is the probability of *A* or *B* occurring? What is the probability that neither occurs?

*Probability of a Union II* (*): Consider the probability associated with the two events *A* and *B*, i.e., *Pr(A)=0.45* and *Pr(B)=0.3*. The probability that both of those events occur at the same time, i.e., \(Pr(A\cap B)\) is 0.2. What is the probability of the union?

*Party* (**): Assume that 52% of the population are Republicans and 48% of the population are Democrats. On a particular issue, 64% of Republicans are in favor and 52% of Democrats are in favor. If you randomly pick a person who is in favor of the issue, what is the probability that the person is a Democrat?

*Smoke Detector* (**): Smoke and fire detectors are essential to save lives. Unfortunately, there are many false fire alarms. Suppose that the probability of an actual fire happening is very low at 5%. Smoke detectors are extremely good at detecting an actual fire, i.e., given a fire, there is a 99% probability that the smoke alarm detects it. If there is no fire, there is a 10% probability that the fire alarm sounds. Suppose that you hear a fire alarm, what is the probability that there is a fire?

*Independence* (**): Suppose you are rolling a die. Consider the events *A* (“rolling an even number”) and *B* (“rolling a number less than four”). Are *A* and *B* independent?