Question

exercise 04.25 (some basic relationships of probability)
a 2018 pew research center survey (pew research website) examined the use of social media platforms in the united states. the survey found that there is a 0.68 probability that a randomly selected american will use facebook and a 0.25 probability that a randomly selected american will use linkedin. in addition, there is a 0.22 probability that a randomly selected american will use both facebook and linkedin.
a. what is the probability that a randomly selected person will use facebook or linkedin (to 2 decimals)?
b. what is the probability that a randomly selected person will not use either social media platform (to 2 decimals)?

Explanation:

Step1: Recall probability formula

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $A$ is the event of using Facebook and $B$ is the event of using LinkedIn. Given $P(A) = 0.68$, $P(B)=0.25$ and $P(A\cap B)=0.22$.

Step2: Calculate $P(A\cup B)$

$P(A\cup B)=0.68 + 0.25- 0.22=\frac{68}{100}+\frac{25}{100}-\frac{22}{100}=\frac{68 + 25-22}{100}=\frac{71}{100}=0.71$

Step3: Calculate the probability of not using either

The probability of not using either is $P(\overline{A\cup B})=1 - P(A\cup B)$. Since $P(A\cup B)=0.71$, then $P(\overline{A\cup B})=1 - 0.71 = 0.29$

Answer:

a. 0.71
b. 0.29