Question

Given that the P(A) = .3, P(B) = .5 and P(AnB) = .25, decide if the

events are independent? Justify your answer.

Answer 1

A and B are not independent

Step-by-step explanation:

Given

`P(A) = .3,`

`P(B) = .5`

`P(A\ n\ B) = .25`

Required

Determine if A and B are independent

If A and B are independent, then:

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

Substitute values for P(A) and P(B)

`P(A\ n\ B) = .3 * .5`

`P(A\ n\ B) = .15`

The calculated value of P(A n B) and the given value of P(A n B) are not equal.

i.e.

`.15 \\e .25`

Hence, A and B are not independent