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The information given is related to data on incoming patients into the hospital.

According to the given information,

Let $1$be that the patient has insurance and $0$be that the patient do no has insurance.

Let the condition of patient be -

Good - $g$

Fair - $f$

Serious - $s$

Therefore, the sample space $S$localid="1649317437417" role="math" $=\left\{\left(1,g\right),\left(1,f\right),\left(1,s\right),\left(0,g\right),\left(0,f\right),\left(0,s\right)\right\}$

Let $1$ be that the patient has insurance and $0$ be that the patient do no has insurance.

Let the condition of patient be -

Good - $g$

Fair - $f$

Serious - $s$

The event $A$represents the patients in serious condition.

So the outcomes in$A$will berole="math" localid="1649317522513" $\left\{\left(1,s\right),\left(0,s\right)\right\}$

Let $1$be that the patient has insurance and $0$be that the patient do no has insurance.

Let the condition of patient be -

Good - $g$

Fair - $f$

Serious - $s$

The event $B$represents the uninsured patients.

So the outcomes in $B$will berole="math" localid="1649317460339" $\left\{\left(0.g\right),\left(0,f\right),\left(0,s\right)\right\}$

We have,

$$\begin{gathered} S=\left\{\left(1,g\right),\left(1,f\right),\left(1,s\right),\left(0,g\right),\left(0,f\right),\left(0,s\right)\right\} \\ B=\left\{\left(0.g\right),\left(0,f\right),\left(0,s\right)\right\} \\ A=\left\{\left(1,s\right),\left(0,s\right)\right\} \\ ⇒B^c=\left\{\left(1,g\right),\left(1,f\right),\left(1,s\right)\right\} \\ {B}^c∪A=\left\{\left(1,g\right),\left(1,f\right),\left(1,s\right),\left(0,s\right)\right\} \end{gathered}$$