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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.

User Roetzi
by
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1 Answer

1 vote

Answer:

Independent events

Explanation:

Given


P(A) = 0.50


P(B)= 0.70


P(A\ u\ B) = 0.85

Required

Determine the relationship between the events

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


P(A\ n\ B) = P(A) * P(B)

and


P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)

So, we have:


P(A\ n\ B) = P(A) * P(B)


P(A\ n\ B) = 0.50 * 0.70


P(A\ n\ B) = 0.35

and


P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)


P(A\ n\ B) = 0.50 + 0.70 - 0.85


P(A\ n\ B) = 0.35

Since:
P(A\ n\ B) = P(A) * P(B)
= 0.35

Then: the events are independent

User RedBassett
by
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