Independent and Dependent Events Examples Page 1

Two dice are rolled. Using the formal definition of independence, determine whether events A and B are independent or dependent.

A: Rolling 1 on the first die.
B: The dice summing to 8.

First we find the probability of each event. We know that

and using the table in the previous example,

.

The probability of both A and B happening is 0, since there is no way to roll 1 on the first die AND have the dice sum to 8. Your father may have told you that anything is possible if you put your mind to it, but apparently he never envisioned this scenario. So

probability of A and B = 0,

Since

events A and B are dependent.