Answer
$P(at~least~one~auto~racing~fan~prefers~NASCAR)=0.97174239$
Work Step by Step
The event "at least one auto racing fan prefers NASCAR" is the complement of "none of the four auto racing fans prefers NASCAR". Using the Complement Rule (see page 275):
$P(at~least~one~auto~racing~fan~prefers~NASCAR)=1-P(none~of~the~four~auto~racing~fans~prefers~NASCAR)=1-0.02825761=0.97174239$