Answer
$D'\cup A$
8
Work Step by Step
$A$:the red die shows a 1.
$D$: the numbers do not add to 11
$A\cap D'$ is an empty set because if the red die shows a 1, the numbers can not add to 11.)
Either he numbers add to 11 or the red die shows a 1.: $D'\cup A$
$D'=${(5,6)(6,5)}
$A=${{1,1},(1,2),(1,3),(1,4),(1,5),(1,6)}
$n(D'\cup A)=n(D')+n(A)=2+6=8$
