Answer
$P(at~least~one~auto~racing~fan~does~not~prefer~NASCAR)=0.87883$
Work Step by Step
The event "at least one auto racing fan does not prefer NASCAR" is the complement of "four auto racing fans prefer NASCAR".
Using the Complement Rule (see page 275):
$P(at~least~one~auto~racing~fan~does~not~prefer~NASCAR)=1-P(four~auto~racing~fans~prefer~NASCAR)=1-0.12117=0.87883$
