Answer:
A and B are not independent
Explanation:
Given
[tex]P(A) = .3,[/tex]
[tex]P(B) = .5[/tex]
[tex]P(A\ n\ B) = .25[/tex]
Required
Determine if A and B are independent
If A and B are independent, then:
[tex]P(A\ n\ B) = P(A) * P(B)[/tex]
Substitute values for P(A) and P(B)
[tex]P(A\ n\ B) = .3 * .5[/tex]
[tex]P(A\ n\ B) = .15[/tex]
The calculated value of P(A n B) and the given value of P(A n B) are not equal.
i.e.
[tex].15 \ne .25[/tex]
Hence, A and B are not independent
