In the following exercise, list the simple events associated with each experiment.

An opinion poll is conducted among a group of registered voters. Their political affiliationDemocrat $(D)$, Republican $(R)$, or Independent $(I)$-and their sex-male $(m)$ or female $(f)$-are recorded.

Fill in the blanks.

A sample space in which the outcomes are equally likely is called a/an _____ sample space; if such a space contains n simple events, then the probability of each simple event is _____.

What is wrong with the following statement? There are eight grades in Garfield Elementary School. If a student is selected at random from the school, then the probability that the student is in the first grade is $\frac{1}{8}$.

Let E and F be two mutually exclusive events, and suppose P(E)=.35 and P(F)=.47. Find:

a. $P\left(F^c\right)$

b. $P\left(E \cap F^c\right)$

c. $P(E \cup F)$

d. $P\left(E^c \cap F^c\right)$

In the following exercise, let S={a, b, c, d, e, f} be a sample space of an experiment, and let E={a, b}, F={a, d, f}, and G={b, c, e} be events of this experiment.

Find the events $F^c$ and $E \cap G^c$.

Refer to the earlier question. If E is the event that a product was produced in Factory A, Factory B, or Factory C and $P(E) \neq 0$, what does $P(A \mid E)$ represent?

A tax specialist has estimated that the probability that a tax return selected at random will be audited is .02. Furthermore, he estimates that the probability that an audited return will result in additional assessments being levied on the taxpayer is .60. What is the probability that a tax return selected at random will result in additional assessments being levied on the taxpayer?

A pair of dice is rolled, and the number that appears uppermost on each die is observed. In the following exercise, refer to this experiment, and find the probability of the given event.

A pair of $1 \mathrm{~s}$ is thrown.

If A and B are events in an experiment and the conditional probability $P(B \mid A)$ is known, give the formula that can be used to compute the probability of the event that both A and B will occur.

An unbiased coin is tossed five times. In the following exercise, find the probability of the given event.

The coin lands heads at least once.

In a survey conducted by USA Today in the week of August 20,2012, the following question was asked: Where do you stay when you visit national parks? The results of the survey follow:

What is the probability that a randomly chosen participant in the survey said that he or she would:

a. Stay in a nearby campground or RV park?

b. Stay in an in-park lodge or an in-park campground?

c. Not stay in a nearby hotel or motel

If a card is drawn at random from a standard 52-card deck, what is the probability that the card drawn is:

a. A diamond?

b. A black card?

c. An ace?

A die is rolled, and the number that falls uppermost is observed. Let E denote the event that the number shown is a 2, and let F denote the event that the number shown is an even number.

a. Are the events E and F mutually exclusive?

b. Are the events E and F complementary?

A study was conducted among a certain group of union members whose health insurance policies required second opinions prior to surgery. Of those members whose doctors advised them to have surgery, $20 \%$ were informed by a second doctor that no surgery was needed. Of these, $70 \%$ took the second doctor's opinion and did not go through with the surgery. Of the members who were advised to have surgery by both doctors, $95 \%$ went through with the surgery. What is the probability that a union member who had surgery was advised to do so by a second doctor?