Suppose that we have a sample space $S = \{e_1, e_2, e_3, e_4, e_5, e_6\}$, where $e_i$ denote the sample points. The following probability assignments apply: $P(e_1) = 0.2$, $P(e_2) = 0.15$, $P(e_3) = 0.25$, $P(e_4) = 0.05$, $P(e_5) = 0.25$, and $P(e_6) = 0.1$. Let
$A = \{e_1, e_2, e_3, e_4\}$
$B = \{e_2, e_3, e_5\}$
$C = \{e_3, e_4, e_5, e_6\}$
(a) Find $P(A)$, $P(B)$, and $P(C)$.
$P(A) = \boxed{0.6}$
$P(B) = \boxed{0.6}$
$P(C) = \boxed{0.7}$
(b) Find $A \cup B$. (Enter your answer in set notation.)
$A \cup B = \boxed{\{e_1, e_2, e_3, e_4, e_5\}}$
$P(A \cup B) = \boxed{0.9}$
(c) Find $A \cap B$. (Enter your answer in set notation.)
$A \cap B = \boxed{\{e_2, e_3\}}$
(d) Are events A and C mutually exclusive?
They \boxed{are not} mutually exclusive.
