Question

(a) if an adult american is randomly selected, what is the probability they use social media?
p(use social media) = 0.641
(round to three decimal places as needed.)
(b) if an adult american is randomly selected, what is the probability they are 45 to 54 years of age?
p(45 - 54) = 0.270
(round to three decimal places as needed.)
(c) if an adult american is randomly selected, what is the probability they are a 35 - to 44 - year - old social media user?
p(35 - 44 and use social media) = 0.175
(round to three decimal places as needed.)
(d) if an adult american is randomly selected, what is the probability they are 35 to 44 years old or use social media?
p(35 - 44 or use social media) =
(round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for \(P(A\ or\ B)\)

The formula for \(P(A\ or\ B)\) is \(P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)\). Let \(A\) be the event of being \(35 - 44\) years old and \(B\) be the event of using social media.

Step2: Find \(P(35 - 44)\)

\(P(35 - 44)=\frac{123}{504}\approx0.244\) (since there are \(123\) people in the \(35 - 44\) age - group out of a total of \(504\) people).

Step3: Find \(P(\text{use social media})\)

\(P(\text{use social media})=\frac{323}{504}\approx0.641\) (given in part (a)).

Step4: Find \(P(35 - 44\ and\ use\ social\ media)\)

\(P(35 - 44\ and\ use\ social\ media)=\frac{88}{504}\approx0.175\) (given in part (c)).

Step5: Calculate \(P(35 - 44\ or\ use\ social\ media)\)

Substitute the values into the formula: \(P(35 - 44\ or\ use\ social\ media)=P(35 - 44)+P(\text{use social media})-P(35 - 44\ and\ use\ social\ media)\)
\(P(35 - 44\ or\ use\ social\ media)=\frac{123 + 323-88}{504}=\frac{358}{504}\approx0.710\)

Answer:

\(0.710\)