Which statement is true about whether z and b are independent events?

z and b are independent events because p(z∣b) = p(z).
z and b are independent events because p(z∣b) = p(b).
z and b are not independent events because p(z∣b) ≠ p(z).
z and b are not independent events because p(z∣b) ≠ p(b).

Two events Z and B are said to be independent if event Z occuring does not prevent event B from happening. Then P(Z and B) = P(Z) · P(B)

Conditional event, P(Z | B) is given by P(Z and B)/P(B) = P(Z) · P(B) / P(B) = P(Z)

Now, P(Z | B) = P(Z and B) / P(B) = 126/280 = 0.45 and P(Z) = 297/660 = 0.45

Therefore, Z and B are independent events because P(Z∣B) = P(Z).