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) =
(round to three decimal places as needed.)

Explanation:

Step1: Calculate \( P(\text{uses social media}|\text{35 - 44 years}) \)

Use the formula \( P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{n(A\cap B)}{n(B)} \).
Here, \( n(A\cap B) = 86 \) (number of people who use social media and are in 35 - 44 years group), \( n(B)=121 \) (total number of people in 35 - 44 years group).
So, \( P(\text{uses social media}|\text{35 - 44 years})=\frac{86}{121} \).

Step2: Simplify the fraction

\( \frac{86}{121}\approx0.711 \) (rounded to three decimal places).

Answer:

\( P(\text{uses social media}|\text{35 - 44 years})\approx0.711 \)