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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 from the reading,
The probability of both A and B happening is 0, since there's no way to roll 1 on the first die AND have the dice sum to 8 (the most we can roll on the second die is 6, and 1 + 6 is only 7). 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 we can say
probability of A and B = 0.
Are they dependent or independent, though?
They're not equal, so events A and B are dependent.