Answer
$P(none~of~the~four~auto~racing~fans~prefers~NASCAR)=0.02825761$
Work Step by Step
$59$% $=0.59$
$P(auto~racing~fan~prefers~NASCAR)=0.59$
The event "auto racing fan does not prefer NASCAR" is the complement of "auto~racing~fan~prefers~NASCAR". Using the Complement Rule (see page 275):
$P(auto~racing~fan~does~not~prefer~NASCAR)=1-P(auto~racing~fan~prefers~NASCAR)=1-0.59=0.41$
Using the Multiplication Rule (see page 282):
$P(none~of~the~four~auto~racing~fans~prefers~NASCAR)=P(auto~racing~fan~1~does~not~prefer~NASCAR)\times P(auto~racing~fan~2~does~not~prefer~NASCAR)\times P(auto~racing~fan~3~does~not~prefer~NASCAR)\times P(auto~racing~fan~4~does~not~prefer~NASCAR)=0.41\times0.41\times0.41\times0.41=0.02825761$
