91Ó°ÊÓ

It is given that, A, B, and C take turns flipping a coin. The first one to get a head wins.

The given sample space is

$S=\left\{\begin{array}{l}1,01,001,0001,...,\\ 0000···\end{array}\right.$

$1$: A wins on first throw.

$01$: A does not get head, B gets head and win.

role="math" localid="1649255091122" $001$: A and B do not get head, C gets head and win.

$0001$: A, B, and C do not get head, A gets head in fourth toss and win.

$0000...$: A, B, and C do not get head in repeated throws.

A can win in first throw or in fourth throw or in seventh throw and so on.

B can win in second throw or in fifth throw or in eighth throw and so on.

Therefore, $S_B=\left\{\left(0,1\right),\left(0,0,0,0,1\right),\left(0,0,0,0,0,0,0,1\right),.........\right\}$

$S_A=\left\{\left(1\right),\left(0,0,0,1\right),\left(0,0,0,0,0,0,1\right),.........\right\}$

$S_B=\left\{\left(0,1\right),\left(0,0,0,0,1\right),\left(0,0,0,0,0,0,0,1\right),.........\right\}$

$S_{{\left(A∪B\right)}^c}=$A or B do not win.

Therefore, $S_{{\left(A∪B\right)}^c}=\left\{\left(0,0,1\right),\left(0,0,0,0,0,1\right),\left(0,0,0,0,0,0,0,0,1\right),.........\right\}$