Question

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).

Answer 1

The answer is the first one im taking that test rn lol

Answer 2

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

Explanation:

Z and B are independent events

When Z and B are independent events then

P(Z and B) = P(Z) * P(B)

P(Z∣B)=
`(P(Z and B))/(P(B))`

P(Z∣B)=
`(P(Z)*P(B))/(P(B))`

We cancel out P(B) on both sides

P(Z|B) = P(Z)