Question

a survey shows that 70% of teenagers own smartphones. among smartphone owners, 80% use social media daily. among non - smartphone owners, 20% use social media daily. are smartphone ownership and daily social media use independent?
yes, because both percentages are given
no, because p(social media | smartphone) ≠ p(social media | no smartphone)
yes, because the events can both happen
cannot determine without knowing the total sample size

Explanation:

Step1: Recall the definition of independence

Two events $A$ (smartphone ownership) and $B$ (daily social - media use) are independent if $P(B|A)=P(B|\overline{A})$.

Step2: Analyze the given probabilities

We are given that $P(B|A) = 0.8$ (probability of using social media daily given smartphone ownership) and $P(B|\overline{A})=0.2$ (probability of using social media daily given non - smartphone ownership). Since $0.8
eq0.2$, the two events are not independent.

Answer:

B. No, because P(social media | smartphone) $
eq$ P(social media | no smartphone)