A sample space, $S$, yields four simple events, $A, B, C$, and $D$, such that $P(A)=0.35, P(B)=$ $0.10$, and $P(C)=0.25$.

a. Find $P(D)$.

b. Find $P\left(C^C\right)$.

c. Find $P(A \cup B)$.

You roll a die with the sample space $S=\{1,2,3,4,5,6\}$. You define $A$ as $\{1,2,3\}, B$ as $\{1,2$, $3,5,6\}, C$ as $\{4,6\}$, and $D$ as $\{4,5,6\}$. Determine which of the following events are exhaustive and/or mutually exclusive.

B and C

You roll a die with the sample space $S=\{1,2,3,4,5,6\}$. You define $A$ as $\{1,2,3\}, B$ as $\{1,2$, $3,5,6\}, C$ as $\{4,6\}$, and $D$ as $\{4,5,6\}$. Determine which of the following events are exhaustive and/or mutually exclusive.

A and D