Jrock0719
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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).

Which statement is true about whether Z and B are independent events Z and B are independent events because PZB PZ Z and B are independent events because PZB PB class=

Respuesta :

nobillionaireNobley
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).

Independent events are the event whose occurrences does not repents on the other events.

The event Z and B are independent events because,

[tex]P(Z|B) = P(Z).[/tex]

Thus the option one is the correct option.

What is independent events?

Independent events are the event whose occurrences does not repents on the other events.

For the independent events the outcome of first event does not affect the outcome of other events. Both event occurrences is free from each other.

As the Z and B are the two events. Then,

[tex]P(Z)*P(B)=P(Z).P(B)[/tex]

For the event B,

[tex]P(Z|B) = \dfrac{P(Z).P(B)}{P(B)} \\P(Z|B) = \dfrac{126}{260} \\P(Z|B) =0.45[/tex]

Hence the event Z and B are independent events because,

[tex]P(Z|B) = P(Z).[/tex]

Thus the option one is the correct option.

Learn more about the independent events here;

https://brainly.com/question/13797498

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