A single fair die is rolled. What if event A stays the same, i. e., A={2,4} but B={2,4,5}. Event A is independent with event B. True or False?

False.

Event A and event B are not independent.

Step-by-step explanation:

We know that event A and event B are

A = {2,4} and B = {2,4,5}.

If the following condition satisfies then event A and event B are independent:

P (A and B) = P (A) * P (B).

Now A and B=?

A and B=A∩B = {2,4} ∩ {2,4,5}

A and B=A∩B={2,4}

The single fair die results in 6 outcomes so, the sample space will contain 6 elements.

Thus,

P (A∩B) = 2/6=1/3

P (A) = 2/6=1/3

P (B) = 3/6=1/2

P (A) * P (B) = 1/3*1/2=1/6

As,

P (A∩B) ≠P (A) * P (B)

1/3≠1/6

Thus, events A and event B are dependent.