Question

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

Answer 1

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