Each student in the Junior class was asked if they had to complete chores at home and if they had a curfew. The table represents the data.

Question

Each student in the Junior class was asked if they had to complete chores at home and if they had a curfew. The table represents the data.

	Yes Curfew	No Curfew	Totals
Yes Chores	51	24	75
No Chores	30	12	42
Totals	81	36	117

Let:

Event A = Having a curfew

Event B = Having chores

 

Which statement accurately describes this data?

A. A & B are are not independent because P(A | B) = 51/75 and the P(A) = 75/117 are not equal.

B. A & B are independent because P(A | B) = 51/75 and the P(A) = 75/117 are equal.

C. A & B are independent because P(A | B) = 51/81 and the P(A) = 81/117 are equal.

D. A & B are not independent because P(A | B) = 51/81 and the P(A) = 81/117 are not equal.

Please Help! I have to turn this in soon!

Answer 1

Use the conditional probability formula.

P(A|B) = P(A ∩ B)/P(B) = (51/117)/(75/117) = 51/75 ≠ 81/117 = P(A)

Choice C is the correct answer.