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

Question

asked Jan 14, 2022 16.3k views

1 Answer

RedBassett · Answer 1 · 2022-01-19T23:40:57+0000

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