Answer:
(a) The probability that a randomly selected U.S. adult uses social media is 0.35.
(b) The probability that a randomly selected U.S. adult is aged 18–29 is 0.22.
(c) The probability that a randomly selected U.S. adult is 18–29 and a user of social media is 0.198.
Step-by-step explanation:
Denote the events as follows:
<em>X</em> = an US adult who does not uses social media.
<em>Y</em> = an US adult between the ages 18 and 29.
<em>Z</em> = an US adult between the ages 30 and above.
The information provided is:
P (X) = 0.35
P (Z) = 0.78
P (Y ∪ X') = 0.672
(a)
Compute the probability that a randomly selected U.S. adult uses social media as follows:
P (US adult uses social media (<em>X'</em><em>)</em>) = 1 - P (US adult so not use social media)
![=1-P(X)\\=1-0.35\\=0.65](https://tex.z-dn.net/?f=%3D1-P%28X%29%5C%5C%3D1-0.35%5C%5C%3D0.65)
Thus, the probability that a randomly selected U.S. adult uses social media is 0.35.
(b)
Compute the probability that a randomly selected U.S. adult is aged 18–29 as follows:
P (Adults between 18 - 29 (<em>Y</em>)) = 1 - P (Adults 30 or above)
![=1-P(Z)\\=1-0.78\\=0.22](https://tex.z-dn.net/?f=%3D1-P%28Z%29%5C%5C%3D1-0.78%5C%5C%3D0.22)
Thus, the probability that a randomly selected U.S. adult is aged 18–29 is 0.22.
(c)
Compute the probability that a randomly selected U.S. adult is 18–29 and a user of social media as follows:
P (Y ∩ X') = P (Y) + P (X') - P (Y ∪ X')
![=0.22+0.65-0.672\\=0.198](https://tex.z-dn.net/?f=%3D0.22%2B0.65-0.672%5C%5C%3D0.198)
Thus, the probability that a randomly selected U.S. adult is 18–29 and a user of social media is 0.198.