Question

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

Answer 1

Answer:

Independent events

Step-by-step 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