Answer
$P(at~least~one~is~a~marijuana~user)=0.52541679$
Work Step by Step
$17$% $=0.17$
$P(18-to~25-year-olds~is~marijuana~user)=0.17$
The event "18-to 25-year-olds is not marijuana user" is the complement of "18-to 25-year-olds is marijuana user".
Use the Complement Rule (page 275):
$P(18-to~25-year-olds~is~not~marijuana~user)=1-P(18-to~25-year-olds~is~marijuana~user)=1-0.17=0.83$
$P(none~of~the~4~is~marijuana~user)=P(18-to~25-year-olds~1~is~not~marijuana~user~and~18-to~25-year-olds~2~is~not~marijuana~user~and~18-to~25-year-olds~3~is~not~marijuana~user~and~18-to~25-year-olds~4~is~not~marijuana~user)$
1) not a single event
2) AND
3) independent events
Use the Multiplication Rule for Independent Events (page 282):
$P(none~of~the~4~is~marijuana~user)=P(18-to~25-year-olds~1~is~not~marijuana~user~and~18-to~25-year-olds~2~is~not~marijuana~user~and~18-to~25-year-olds~3~is~not~marijuana~user~and~18-to~25-year-olds~4~is~not~marijuana~user)=P(18-to~25-year-olds~1~is~not~marijuana~user)\times P(18-to~25-year-olds~2~is~not~marijuana~user)\times P(18-to~25-year-olds~3~is~not~marijuana~user)\times P(18-to~25-year-olds~4~is~not~marijuana~user)=0.83\times0.83\times0.83\times0.83=0.47458321$
The event "at least one is a marijuana user" is the complement of "none of the 4 is marijuana user".
Use the Complement Rule (page 275):
$P(at~least~one~is~a~marijuana~user)=1-P(none~of~the~4~is~marijuana~user)=1-0.47458321=0.52541679$
