Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i.
The number of all possible ordered pair (I,j) for which the events `A_(i) and a_(j)` are independent is

Options

A. 6
B. 12
C. 13
D. 25

Answer

D

Explanation

Note that `A_(1)` is independent with all events `A_(1),A_(2),A_(3),A_(4)....,A_(12),` Now, total number of ordered pairs is 23.
`underset(22)( underbrace((1.1),(1,2),(1.3),...,(1,11)))+(1,12)`
Also that `A_(2),A_(3),andA_(3),A_(2)` are independent. Hence, there are 25 ordered pairs.