Question

Two fair dice are thrown independently. Three events A, B and C is defined as

follows :

A: Even face with first dice.

B: Even face with second dice.

C: Sum of the points on the two dice is odd.

Discuss the independence of events A, B and C.

Answer 1

Probability for independent events A and B:

$P(A\land B)=P(A)\cdot P(B)$

We have:

$P(A)=1/2,P(B)=1/2$

$P(A\land B)=1/4$

So, Events A and B are independent.

$P(A\land C)=1/4$

$P(A)\cdot P(C)=1/2\cdot1/2=1/4$

So, Events A and C are independent. The same is for events B and C.

But:

$P(A\land B\land C)=0\ne P(A)\cdot P(B)\cdot P(C)$

So, Events A, B and C are dependent.