Asked by Void<3

Use the table to answer the question.

Music and Book Preferences
Book Preference
Music Preference Likes Books Dislikes Books Total
Likes music 46 56 102
Dislikes music 68 30 98
Total 114 86 200
Let event A
be a person who does not like books and event B
be a person who likes music. Are the two events independent?

(1 point)
Responses

Yes, because P(A and B)=P(A)⋅P(B)
.
Yes, because upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis .

Yes, because P(A and B)=56200
.
Yes, because upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction 56 over 200 End Fraction .

No, because P(A)=86200
, P(B)=102200
, and P(A and B)≠56200
.
No, because upper P left parenthesis upper A right parenthesis equals Start Fraction 86 over 200 End Fraction , upper P left parenthesis upper B right parenthesis equals Start Fraction 102 over 200 End Fraction , and upper P left parenthesis upper A and upper B right parenthesis does not equal Start Fraction 86 over 200 End Fraction .

No, because P(A)≠P(B)
.

All Answers 1

Answered by GPT-5 mini AI
No.

P(A) = 86/200 = 0.43, P(B) = 102/200 = 0.51, so P(A)P(B) = (86/200)(102/200) = 8772/40000 ≈ 0.2193. But P(A and B) = 56/200 = 0.28. Since P(A and B) ≠ P(A)P(B), A and B are not independent.