HSS.CP Tutor Intake - Events, Independence, Conditional Probability, and the Rules of Probability

For a single roll of a fair die, let $A = \{2, 4, 6\}$ (even) and
$B = \{4, 5, 6\}$ (greater than 3). Which outcomes make up the event
"$A$ and $B$" (the intersection $A \cap B$)?

Two events $A$ and $B$ each have positive probability. Which statement
correctly distinguishes independent events from mutually exclusive
events?

A club will choose 3 of its 10 members. In which situation does the
order of selection matter, so that you would count arrangements
(a permutation) rather than unordered selections (a combination)?

Events $A$ and $B$ satisfy $P(A \cap B) = 0.12$ and $P(B) = 0.3$.
Compute the conditional probability $P(A \mid B)$. Give a decimal.

For events $A$ and $B$, $P(A) = 0.5$, $P(B) = 0.4$, and
$P(A \cap B) = 0.2$. Are $A$ and $B$ independent, and why?

A fair die is rolled once. Let $A$ be "the result is even" and $B$ be
"the result is greater than 3." Working from the outcomes directly,
compute $P(A \mid B)$ as a fraction.

One card is drawn from a standard 52-card deck. Using the Addition
Rule, compute $P(\text{king or heart})$ as a fraction.
(There are 4 kings, 13 hearts, and 1 king of hearts.)

Two cards are drawn from a standard 52-card deck WITHOUT replacement.
Compute the probability that both are kings, as a fraction. (Leave the
numerator and denominator unmultiplied if you wish, e.g. write it as a
product of two fractions.)