Solution

Let 

$C_1, C_2$ be the two cold tablets and $A_1,A_2$ be the two aspirin tablets.

Let $xy$ represent the simple event that that $x$ and $y$ are swallowed by first and second patient, respectively.

a. Sample space, S​={A1​A2​,C1​A1​,​A1​C1​,C1​A2​,​A1​C2​,C1​C2​,​A2​A1​C2​A1​,​A2​C1​,C2​A2​,​A2​C2​,C2​C1​​}​

b. The event $A$ that first patient obtained cold tablet contains events where $x \in \{C_1, C_2\}.$

$$\begin{align*} A&=\left\{ \begin{matrix} C_1A_1,& C_1A_2,& C_1C_2, & C_2A_1,& C_2A_2,& C_2C_1 \end{matrix} \right\}\\ \end{align*}$$

c. The event $B$ that exactly one patient obtained cold tablet contains simple events where $x \in \{ C_1 , C_2\}$ or $y \in \{ C_1 , C_2\}$, not both.

$$\begin{align*} B&=\left\{ \begin{matrix} C_1A_1,& C_1A_2, & C_2A_1,& C_2A_2,& A_1C_1 , & A_1C_2, & A_2C_1,& A_2C_2 \end{matrix} \right\}\\ \end{align*}$$

d. The event $C$ is that neither patient gets a cold tablet.

$$\begin{align*} C=\left\{ \begin{matrix} A_1A_2, &A_2A_1 \end{matrix} \right\}\\ \end{align*}$$

Answer