What is the number of undirected graphs that can be formed on a set of $n = 4 labeled vertices$?
There are C(4,2)=6 possible undirected edges, each independently present or absent: $2^6$=64.
What is the number of directed graphs without self-loops that can be formed on $n = 3 labeled vertices$?
There are 3*(3-1)=6 possible directed edges without loops, giving $2^6$=64 graphs.
How many proper subsets does a set of cardinality 6 have?
A 6-element set has $2^6$=64 subsets; excluding the set itself leaves 63 proper subsets.
If A and B are independent events with P(A) = 0.3 and P(B) = 0.6, what is P(A n B)?
For independent events, P(A n B) = P(A) * P(B) = 0.3 * 0.6 = 0.18.
If a fair 6-sided die is rolled 4 times, what is the variance Var(X) of the number of times a '6' is obtained?
Binomial distribution with $n=4$, $p=1/6$, $q=5/6$. Var(X) = n*p*$q = 4 \cdot (1/6) \cdot (5/6) = 20 / 36 = 5 / 9 \approx 0.5556$.