Question

Which statement is true about whether Z and B are independent events?

Answer 1

The correct answer is:

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

Z and B are independent events because P(Z∣B) = P(Z) is true about whether Z and B are independent events.

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Answer 2

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).