Question

a news portal surveyed registered users about whether they prefer to get their news from text articles or from videos on the portal. the data about respondents ages and preferences.

	age below 20	age 20 or above	total
videos	32	90	122
total	48	135	183

which statement is correct?
a. a respondent preferring videos and a respondent preferring text articles are independent events.
b. a respondent preferring text articles and a respondent being younger than 20 are independent events.
c. a respondent preferring text articles and a respondent being 20 or older are dependent events.
d. a respondent preferring videos and a respondent being younger than 20 are dependent events.

Explanation:

Step1: Recall independence formula

For two events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\) for independence.

Step2: Check option C

Let \(A\) be preferring text articles (\(P(A)=\frac{61}{183}\)), \(B\) be being 20 or older (\(P(B)=\frac{135}{183}\)), \(P(A\cap B)=\frac{45}{183}\). And \(\frac{61}{183}\times\frac{135}{183}
eq\frac{45}{183}\), so they are dependent.

Answer:

C. A respondent preferring text articles and a respondent being 20 or older are dependent events.