Question

adult americans (18 years or older) were asked whether they used social media (facebook, twitter, and so on) regularly. the accompanying table is based on a subset of the results of that survey. using the results of the survey, determine p(uses social media) and p(uses social media | 35 - 44 years). are the events uses social media and 35 - 44 years independent?

p(uses social media) = 0.636
(round to three decimal places as needed.)

p(uses social media | 35 - 44 years) = 0.711
(round to three decimal places as needed.)

are the events uses social media and 35 - 44 years independent? choose the correct answer.

a. yes, because p(uses social media) and p(uses social media | 35 - 44 years) are not equal.

b. no, because p(uses social media) and p(uses social media | 35 - 44 years) are equal.

c. yes, because p(uses social media) and p(uses social media | 35 - 44 years) are equal.

d. no, because p(uses social media) and p(uses social media | 35 - 44 years) are not equal.

Explanation:

Step1: Recall the definition of independent events

Two events \(A\) and \(B\) are independent if \(P(A)=P(A|B)\)

Step2: Compare the probabilities

We are given \(P(\text{uses social media}) = 0.636\) and \(P(\text{uses social media}|35 - 44\text{ years})=0.711\)

Since \(0.636
eq0.711\), that is \(P(\text{uses social media})
eq P(\text{uses social media}|35 - 44\text{ years})\)

Answer:

D. No, because \(P(\text{uses social media})\) and \(P(\text{uses social media }|35 - 44\text{ years})\) are not equal.