Question

A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 45, 20, 25, 90. The third column is labeled Y with entries 30, 10, 35, 75. The fourth column is labeled Z with entries 60, 25, 50, 135. The fifth column is labeled Total with entries 135, 55 110, 300.
Which statement is true about whether C and Y are independent events?

C and Y are independent events because P(C∣Y) = P(Y).
C and Y are independent events because P(C∣Y) = P(C).
C and Y are not independent events because P(C∣Y) ≠ P(Y).
C and Y are not independent events because P(C∣Y) ≠ P(C).

Answer 1

P(C) = 110/300 = 11/30 ≈ 0.3667.
P(C|Y) = 35/75 = 7/15 ≈ 0.4667.

Since P(C|Y) ≠ P(C), C and Y are not independent. (So the correct statement is the fourth one.)