Toss two different standard dice, white and black.

The sample space S of the outcomes consists of all ordered pairs ij, i,j=1,2, …,6

S={(1,1), (1,2), (1,3), …, (6,6)}

Each point in S has probability 1/36

Let

A={first die=1,2 or 3}

B={first die=3,4 or 5}

C={sum of faces is 9}

AB={31,32,33,34,35,36}

AC={36}

BC={35,45,54}

ABC={36}

P(A)=P(B)=1/2 P(C)=1/9

P(ABC)=1/36=(1/2)(1/2)(1/9)=P(A)P(B)P(C)

But

P(AB)=1/6 P(A)P(B)=1/4

P(AC)=1/36 P(A)P(C)=1/18

P(BC)=1/12 P(B)P(C)=1/18.