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() = 0.50, () = 0.70, ( ∪ ) = 0.85 Are the events, and , independent in this situation? You must provide reasoning for your answer.

Sagot :

MrRoyalidn

Answer:

Independent events

Step-by-step explanation:

Given

[tex]P(A) = 0.50[/tex]

[tex]P(B)= 0.70[/tex]

[tex]P(A\ u\ B) = 0.85[/tex]

Required

Determine the relationship between the events

To do this, we simply calculate P(A n B) using:

[tex]P(A\ n\ B) = P(A) * P(B)[/tex]

and

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

So, we have:

[tex]P(A\ n\ B) = P(A) * P(B)[/tex]

[tex]P(A\ n\ B) = 0.50 * 0.70[/tex]

[tex]P(A\ n\ B) = 0.35[/tex]

and

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

[tex]P(A\ n\ B) = 0.50 + 0.70 - 0.85[/tex]

[tex]P(A\ n\ B) = 0.35[/tex]

Since: [tex]P(A\ n\ B) = P(A) * P(B)[/tex] [tex]= 0.35[/tex]

Then: the events are independent

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