a news portal surveyed registered users about whether they prefer to get their news from text articles or…

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.\n| | age below 20 | age 20 or above | total |\n|--|--|--|--|\n| text articles | 16 | 45 | 61 |\n| videos | 32 | 90 | 122 |\n| total | 48 | 135 | 183 |\nwhich statement is correct?\na. a respondent preferring videos and a respondent preferring text articles are independent events.\nb. a respondent preferring text articles and a respondent being younger than 20 are independent events.\nc. a respondent preferring text articles and a respondent being 20 or older are dependent events.\nd. a respondent preferring videos and a respondent being younger than 20 are dependent events.

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.\n| | age below 20 | age 20 or above | total |\n|--|--|--|--|\n| text articles | 16 | 45 | 61 |\n| videos | 32 | 90 | 122 |\n| total | 48 | 135 | 183 |\nwhich statement is correct?\na. a respondent preferring videos and a respondent preferring text articles are independent events.\nb. a respondent preferring text articles and a respondent being younger than 20 are independent events.\nc. a respondent preferring text articles and a respondent being 20 or older are dependent events.\nd. a respondent preferring videos and a respondent being younger than 20 are dependent events.

Answer

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}\neq\frac{45}{183}), so they are dependent.

Answer:

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