Answer
The events are independent.
$P(male)=P(male~|~0~activities)$ and $P(0~activities)=P(0~activities~|~male)$
Work Step by Step
The sample space: 400 teens. So, N(S) = 400
N(male) = 200, N(0 activities) = 42 and N(male and 0 activities) = 21. So:
$P(male)=\frac{N(male)}{N(S)}=\frac{200}{400}=0.5$. (Classical Method, page 259.)
$P(0~activities)=\frac{N(0~activities)}{N(S)}=\frac{42}{400}=0.105$. (Classical Method, page 259.)
Now:
$P(male~|~0~activities)=\frac{N(male~and~0~activities)}{N(0~activities)}=\frac{21}{42}=0.5$. (Conditional Rule, page 288.)
$P(0~activities~|~male)=\frac{N(male~and~0~activities)}{N(male)}=\frac{21}{200}=0.105$. (Conditional Rule, page 288.)
$P(male)=P(male~|~0~activities)$ and $P(0~activities)=P(0~activities~|~male).$
The events are independent. See definition, page 292.
