A single fair die is rolled. Let events A={2,4}, and B={1,2,5}. Event A is independent with event B. True or False?

TRUE

Step-by-step explanation:

Event A and event B will be independent if

P (A∩B) = P (A) * P (B)

A={2,4}

B={1,2,5}

There are 6 outcomes when die is rolled.

n (S) = 6

A∩B={2}

P (A∩B) = n (A∩B) / n (S) = 1/6

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

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

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

As,

P (A∩B) = P (A) * P (B)

So, event A and event B are independent.