Question

Use the table to answer the question.

Friction and Non-Friction Preferences of Different Age Groups
Book Preferences by Age Group
Age Group Prefers Fiction Prefers Nonfiction Total
20 to 30 years old 12 3 15
31 to 40 years old 24 6 30
Total 36 9 45
Let event A
be someone who is 31 to 40 years old and event B
represent someone who prefers fiction. Find P(A and B)
and determine if the two events are independent.

(1 point)
Responses

P(A and B)=2445
but does not indicate that the two events are independent.
upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction 24 over 45 End Fraction but does not indicate that the two events are independent.

P(A and B)=6645
and shows that the two events are independent.
upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction 66 over 45 End Fraction and shows that the two events are independent.

P(A and B)=645
and shows that the two events are independent.
upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction 6 over 45 End Fraction and shows that the two events are independent.

P(A and B)=2445
and shows that the two events are independent.

Answer 1

P(A and B) = 24/45 = 8/15.
P(A) = 30/45 = 2/3, P(B) = 36/45 = 4/5, and P(A)P(B) = (2/3)(4/5) = 8/15 = P(A and B).
Therefore the events are independent. (Choose: 24/45 and shows that the two events are independent.)